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矩陣的對角化問題
矩陣的對角化問題
摘要
本文主要討論了矩陣的對角化.根據線性變換 （或 階方陣 ）的特征值將 維線性空間 分解成不變子空間的直和,并對根子空間分解定理給出了3種較為初等的證明.然后運用根子空間分解定理，得出了線性變換 （ 或 階方陣 ）可對角化的充要條件.
關鍵詞: 線性變換；不變子空間；根子空間；直和；分解；可對角化；最小多項式；不變因子.
On The Sum of Matrix Diagonalizable
ABSTRACT
In this paper, we mainly discuss matrix diagonalizable. According as eigenvalue of a linear transformation (or a matrix A of the n-th order), a n-dimensional linear space V decomposes direct sum of invariant subspace. Three elementary proofs is given, for the theorem of root subspace decomposition .Then applying the theorem of root subspace decomposition, it comes to the necessary and sufficient condition of diagonalizable about the linear transformation (or matrix A of the n-th order).
Keywords: linear transformation; invariant subspace; root subspace; direct sum; decomposition; diagonalizable; minimal polynomial; invariant factor.
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