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<p><span class="autocomment">　ユークリッド空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:54時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">47 行:</td> <td colspan="2" class="diff-lineno">47 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ユークリッド空間$(S,V)$における$V$を、$S$に付随する計量空間という。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ユークリッド空間$(S,V)$における$V$を、$S$に付随する計量空間という。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>また$S$の元を点、$V$の元をベクトルという。&lt;br/&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>また$S$の元を点、$V$の元をベクトルという。&lt;br/&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">命題&lt;br/&gt;</del></div></td><td colspan="2">&nbsp;</td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　固有値と固有ベクトル</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:39時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">18 行:</td> <td colspan="2" class="diff-lineno">18 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[wikibooks_ja:線型代数学/<del class="diffchange diffchange-inline">wikibooks_ja(</del>固有値と固有ベクトル|線型代数学/固有値と固有ベクトル)]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[wikibooks_ja:線型代数学/固有値と固有ベクトル|<ins class="diffchange diffchange-inline">wikibooks_ja(</ins>線型代数学/固有値と固有ベクトル)]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　固有値と固有ベクトル</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:37時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">18 行:</td> <td colspan="2" class="diff-lineno">18 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[[wikibooks_ja:線型代数学/固有値と固有ベクトル|線型代数学/固有値と固有ベクトル<del class="diffchange diffchange-inline">(wikibooks_ja</del>)]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[wikibooks_ja:線型代数学/<ins class="diffchange diffchange-inline">wikibooks_ja(</ins>固有値と固有ベクトル|線型代数学/固有値と固有ベクトル)]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　ジョルダンの標準形</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:34時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">21 行:</td> <td colspan="2" class="diff-lineno">21 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　単因子に基ずく方法&nbsp; ===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">*[[wikipedia_ja:ジョルダンの標準形 |ウィキペディア(ジョルダンの標準形 )]]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　幾何学的方法&nbsp; ===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　我々の住む空間の数学的公理化 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　我々の住む空間の数学的公理化 ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>今までの議論をもとに、我々の住む空間の数学的な定義を与える（注参照）。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>今までの議論をもとに、我々の住む空間の数学的な定義を与える（注参照）。&lt;br/&gt;</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　固有値と固有ベクトル</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:30時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">18 行:</td> <td colspan="2" class="diff-lineno">18 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　固有値と固有ベクトル==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　２次形式と2次曲線の分類===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">[[wikibooks_ja:線型代数学/固有値と固有ベクトル|線型代数学/固有値と固有ベクトル(wikibooks_ja)]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　ジョルダンの標準形&nbsp; ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　単因子に基ずく方法&nbsp; ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　単因子に基ずく方法&nbsp; ===</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　計量線形空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:16時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">6 行:</td> <td colspan="2" class="diff-lineno">6 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>定義&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>定義&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Kを実数の集合（実数体）あるいは複素数の集合（複素数体）とする。＜br</del>/&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Kを実数の集合（実数体）あるいは複素数の集合（複素数体）とする。&lt;br</ins>/&gt;<ins class="diffchange diffchange-inline">　　</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K上の線形空間Vの任意の2元$\ x,\ y\ $に対して&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K上の線形空間Vの任意の2元$\ x,\ y\ $に対して&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>内積と呼ぶKの元$(x,y)$　が定まり、次の性質を持つとき、</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>内積と呼ぶKの元$(x,y)$　が定まり、次の性質を持つとき、</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　計量線形空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:15時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">6 行:</td> <td colspan="2" class="diff-lineno">6 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>定義&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>定義&lt;br/&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Kを実数の集合（実数体）あるいは複素数の集合（複素数体）とする。＜br/&gt;</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K上の線形空間Vの任意の2元$\ x,\ y\ $に対して&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K上の線形空間Vの任意の2元$\ x,\ y\ $に対して&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>内積と呼ぶKの元$(x,y)$　が定まり、次の性質を持つとき、</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>内積と呼ぶKの元$(x,y)$　が定まり、次の性質を持つとき、</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　線形空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:10時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">1 行:</td> <td colspan="2" class="diff-lineno">1 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=　線形代数 =</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=　線形代数 =</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>===　線形空間 <del class="diffchange diffchange-inline">&nbsp; </del>===</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>===　線形空間<ins class="diffchange diffchange-inline">(ベクトル空間) </ins>===</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*[[wikipedia_ja:ベクトル空間|ウィキペディア(ベクトル空間)]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*[[wikipedia_ja:ベクトル空間|ウィキペディア(ベクトル空間)]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　線形空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:09時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">2 行:</td> <td colspan="2" class="diff-lineno">2 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　線形空間&nbsp; ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　線形空間&nbsp; ===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>*[[wikipedia_ja:ベクトル空間|ウィキペディア(ベクトル空間)]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>*[[wikipedia_ja:ベクトル空間|ウィキペディア(ベクトル空間)]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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<p><span class="autocomment">　線形空間</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2024年8月23日 (金) 12:08時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">2 行:</td> <td colspan="2" class="diff-lineno">2 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　線形空間 ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　線形空間&nbsp; ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　線形空間&nbsp; ===</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　線形空間の基底と次元 </del> <del class="diffchange diffchange-inline">===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; <ins class="diffchange diffchange-inline">*[[wikipedia_ja:ベクトル空間|ウィキペディア(ベクトル空間)]]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　線形部分空間&nbsp; ===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">===　線形写像とその行列表現 ===</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">====　線形写像の定義&nbsp; ====</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">====　自己共役写像、正規写像、ユニタリ写像&nbsp; ====</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">====　線形空間の基底と線形写像の行列表現&nbsp; ====</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===　計量線形空間===</div></td></tr> <!-- diff generator: internal 2026-04-18 15:09:20 --> </table>

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