# Matrix Eigenvector Simmetris

This post categorized under Vector and posted on June 25th, 2019.

Stack Exchange network consists of 175 Q&A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.Computation of Eigenvectors. Computation of Eigenvectors. Let A be a square matrix of order n and one of its eigenvalues. Let X be an eigenvector of A graphicociated to . We must have This is a linear system for which the matrix coefficient is . Since the zero-vector is a solution the system is consistent. In fact we will in a different page that the structure of the solution set of this system An idempotent matrix is a matrix A such that A2A. We give an example of an idempotent matrix and prove eigenvalues of an idempotent matrix is either 0 or 1.

Symmetric Matrices For a real symmetric matrix all the eigenvalues are real. If only the dominant eigenvalue is wanted then the Rayleigh method maybe used where Q is the square n n matrix whose i th column is the eigenvector q i of A and is the diagonal matrix whose diagonal elements are the corresponding eigenvalues ii i. Note that only diagonalizable matrices can be factorized in this way.Eine symmetrische Matrix ist in der Mathematik eine quadratische Matrix deren Eintrge spiegelsymmetrisch bezglich der Hauptdiagonale sind. Eine symmetrische Matrix stimmt demnach mit ihrer transponierten Matrix berein.

An matrix is said to be symmetrizable if there exists an invertible diagonal matrix and symmetric matrix such that . The transpose of a symmetrizable matrix is symmetrizable since A T ( D S ) T S D D 1 ( D S D ) displaystyle Amathrm T (DS)mathrm T SDD-1(DSD) and D S D displaystyle DSD is symmetric.