Thread: matrix algebra

question: A is an nxn matrix. all column vectors of A are orthogonal each other. the norm of each column vector of A is 1. show the absolute values of all eigenvalues of A that must be 1?

just dont know what orthogonal and eigenvalues mean in this problem.

Originally Posted by fatboy

question: A is an nxn matrix. all column vectors of A are orthogonal each other. the norm of each column vector of A is 1. show the absolute values of all eigenvalues of A that must be 1?

just dont know what orthogonal and eigenvalues mean in this problem.

Two vectors are orthogonal iff their dot product is zero

A vector X is an eigen vector of a matrix A if there exists a scallar k such that:

AX=kX

then k is the eigenvalue corresponding to the eigenvector X.

RonL