special

symmetrical

Eigenvalues and eigenvectors of matrices

Luquan

Xu Zhong

abstract:

Author unit

Northwestern Polytechnical University

Northwestern Polytechnical University

key word

Eigenvalue of matrix

Orthogonal eigenvector

Eigenvalues and eigenvectors

symmetric matrix

Real symmetric matrix

Characteristic problem

Matrix a

Orthogonal transformation

linear algebra

Orthogonal array

Classification number:

O 15 1

DOI:

China hownet: Sun: xusj.0.1997-04-013.

Text snapshot:

Tongji University Linear Algebra 130 page example 10 needs an orthogonal transformation. To transform quadratic form into standard form, we need the eigenvalue of matrix and the unit orthogonal eigenvector. In fact, this matrix r is a kind of matrix with

special

Symmetric matrix. The characteristic problem of this kind of matrix has the following general conclusions. Consider the following situations

special

Symmetric matrix, where a and b are real symmetric matrices of order m, and u is a column vector of dimension m,