Let A be an n n symmetric matrix Decide if the following ar

Let A be an n × n symmetric matrix. Decide if the following are true or false. No justification needed.

(a) A is orthogonally diagonalizable.

(b) The eigenspaces of A are mutually orthogonal, in the sense that the eigenvectors corresponding to different eigenvalues of A are orthogonal.

(c) The dimension of the eigenspace for each eigenvalue of A equals the multiplicity of as a root of the characteristic equation of A.

Solution

(a) true

(b) true

(c) true