- 相關(guān)推薦
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(jù)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(guān)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.
【矩陣的對角化問題】相關(guān)文章：
矩陣對角化及其應(yīng)用10-20
矩陣可對角化的判定條件及推廣論文08-07
矩陣反問題初探09-06
數(shù)學畢業(yè)論文-矩陣可對角化的判定條件及推廣10-04
廣義對稱、反對稱矩陣反問題07-30
求實對稱矩陣特征值問題的分治算法10-21
矩陣方程的自反和反自反矩陣解07-30
矩陣的分解與應(yīng)用10-09