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Teaching the Concept of Eigenvalues: Linear Algebra for Business Majors

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  • Yukari Shirota

Abstract

本稿では，経営学科の学生に固有値の概念を理解させる教授法として，対角行列で表わされる線型変換を初めに与える方法を提案する。そこでは，始めに，固有値とはその拡大操作による各軸方向の拡大率である，という比喩を用いて説明する。ついで，この拡大操作を複数の非直交座標系に対して行う際，基底変換が必要である，と説明する。伝えるべきことは，直感的解釈として，この対角行列で表される拡大マシンの，各軸方向への倍率が固有値であり，２次元の場合，拡大操作行列の２つの列ベクトルの作る面積が行列式であり，その両者の値は基底を変えても不変，ということである。この教授法を使って，主成分分析を比喩的に説明した。主成分分析とは，その分散共分散行列の固有値を求め，固有値を固有ベクトル方向のデータの分散の度合いと解釈する分析法である。固有ベクトル方向に拡大した様子を分析することが，主成分分析の目的である，と説明する。 に

Suggested Citation

  • Yukari Shirota, 2013. "Teaching the Concept of Eigenvalues: Linear Algebra for Business Majors," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 50(1), pages 31-42.
    • Handle: RePEc:abc:gakuep:50-1-3
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