Question

A symmetric matrix is called ____________, if all its Eigen values are strictly positive i.e., greater than zero.

(a) Negative definite

(b) Positive definite

(c) Co- definite

(d) Alternative definite

The question was posed to me in class test.

The query is from Matrix Algebra topic in section Matrix Algebra and Gaussian Elimination of Finite Element Method

Answer 1

Correct choice is (b) Positive definite

Easiest explanation: If all Eigen values of symmetric matrix are positive then the matrix is called as positive definite matrix. A symmetric matrix A of dimension (n x n) is positive definite if, for any non zero vector x = [x1 x2 x3…… xn]^T. That is x^T Ax > 0.