MAT2002 Lecture Notes - Lecture 12: Invertible Matrix, Nostril

• School: Vellore Institute of Technology - VIT
• Department: Mathematics
• Course: MAT2002

Document Summary

Properties of eigen values:: the product of the eigen values of a matrix a is equal to its determinant, if a is singular matrix then at least of the eigen values of a is zero and conversely, if. 2 are eigen values of a matrix a, then n p p. 2 are the eigen values of a-1 . n are the eigen values of ka n are the eigen values k. 1: matrix a and its transpose at have same eigen values. If a and b are similar matrices the a and b have same eigen values: the diagonal entries are the eigen values of diagonal matrices and lower/upper triangular matrices. Eigen values: 2, -1, 7, 8: if a+ib is the eigenvalue of any square matrix then a-ib will also be an. Let a be the square matrix and is its characteristic f ( ) 0 equation, then where, f ( ) a.