抽象n维列向量演绎

Abstract n-dimensional column vector deductive

指出在矩阵乘法运算中容易被忽略的一个小问题;证明全体n维列向量构成一个向量空间;研究由抽象的n维列向量α所派生出的矩阵αTα、ααT的特性以及方阵ααT的行列式、特征值、特征向量和对角化问题;展示了将抽象的n阶方阵ααT对角化的全过程.所得的部分结论可以作为公式使用.

Pointed out that a small problem easily overlooked in the matrix multiplication,ai- ming to prove that all n-dimensional column vector form a vector space, the matrix aTa de- rived by n-dimensional column vector a, the characteristics and the determinant of the square aTa, eigenvalues, eigenvectors and diagonalization. Matrix diagonalization linear algebra course is a very important knowledge point, the article shows the whole process of abstract order matrix aTa diagonalization. Some of the conclusions of the proceeds can be used as for- mula.