Philippine E-Journals

Spectral Theorem: Diagonalizable Symmetric Matrix

Noriebelle Balbontin

Discipline: Education

 

Abstract:

In linear algebra, is the canonical forms of a linear transformation. Given a particularly nice basis for the vector spaces in which one is working, the matrix of a linear transformation may also be particularly nice, revealing some information about how the transformation operates on the vector space.The spectral theorem provides a sufficient criterion for the existence of a particular canonical form. Specifically, the spectral theorem states that if A equals the transpose of A, then A is diagonalizable:there exists an invertible matrix B such that B-1 AB is a diagonal matrix.