三阶实对称矩阵正交对角化的简便方法
삼계실대칭구진정교대각화적간편방법
The Simple Method of Orthogonal Diagonalization for Real Symmetric Matrix of the Third Order
  • 万方数据
    湖州师范学院学报 호주사범학원학보
    Journal of Huzhou Teachers College
    2015年 10期 9-12 ,共4页

    林林%欧阳成

    림림%구양성

    特征值%特征向量%几何特征%正交矩阵 特徵值%特徵嚮量%幾何特徵%正交矩陣
    특정치%특정향량%궤하특정%정교구진
    eigenvalue%eigenvector%geometric feature%orthogonal matrix
    利用属于相异特征值特征向量的几何特征，给出当三阶实对称矩阵具有二重特征值时如何快速将矩阵正交对角化的简便方法，从而有效地规避实对称矩阵正交对角化过程中的复杂计算。通过实例分析阐述了该方法在高等代数、解析几何等方面的应用。
    이용속우상이특정치특정향량적궤하특정，급출당삼계실대칭구진구유이중특정치시여하쾌속장구진정교대각화적간편방법，종이유효지규피실대칭구진정교대각화과정중적복잡계산。통과실례분석천술료해방법재고등대수、해석궤하등방면적응용。
    This paper,using the geometric feature of characteristic vectors corresponding to differ-ent eigenvalues,attempts to put forward a simple method about the orthogonal diagonalization of the third order real symmetric matrix with a double characteristic value,thus effectively avoiding the com-plicated calculation.In addition,the applications of the method in higher algebra and analytic geometry are illustrated through several examples.
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