Types of Matrices and Basic Operations

Types of Matrices and Basic Operations

This lesson covers the following key concepts:

• Definition, order, and equality of matrices
• Types: row, column, square, diagonal, scalar, identity, null, triangular
• Addition, subtraction, scalar multiplication
• Matrix multiplication (row by column, non-commutative)
• Properties of matrix operations
• Positive integral powers of square matrix
• Transpose, conjugate of matrix

Important Formulas

• $$A_{m \times n}: m \text{ rows, } n \text{ columns}$$
• $$AB \text{ possible if columns of A = rows of B}$$
• $$AB \neq BA \text{ (generally)}$$
• $$(A + B)^T = A^T + B^T$$
• $$(AB)^T = B^T A^T$$
• $$(kA)^T = kA^T$$
• $$A^n = A \cdot A \cdot ... \cdot A \text{ (n times)}$$