Real Analysis

Question

Metrix properties

Answer 1

• In a square matrix, the number of rows and columns are equal.
• A square matrix is a diagonal matrix in which non-diagonal elements are zeroes.
• A square matrix is a scalar matrix in which the non-diagonal elements are zeroes, and diagonal elements are the same.
• A matrix in which all non-diagonal elements are zeroes and diagonal elements are 1s is said to be an identity matrix.
• A matrix is a symmetric matrix if A=A^T
• A matrix is skew-symmetric if A=–A^T
• A matrix is an orthogonal matrix; if A×A^T=I
• A matrix is said to be a singular matrix, if |A|=0
• A matrix is said to be idempotent, if A²=A.
• A matrix is said to be involutory, if A²=I