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Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
What is the eigen value of a real symmetric matrix?
The eigen values of a real symmetric matrix are all real.
What is a symmetric matrix?
a square matrix that is equal to its transpose
What is the definition of a skew-Hermitian matrix?
Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.
What is the definition of an anti-symmetric matrix?
The Definition of an Anti-Symmetric Matrix:If a square matrix, A, is equal to its negative transpose, -A', then A is an anti-symmetric matrix.Notes:1. All diagonal elements of A must be zero.2. The cross elements of A must have the same magnitude, but opposite sign.
