B.Sc Method Chapter 3 (Matrices) Notes

Mathematical Methods (B.Sc.)

Chapter:03 (Matrices)

In this chapter, we will study the following topics:

• introduction
• column vector
• upper (lower) triangular matrix
• main diagonal
• identity matrix
• scalar matrix
• equality of matrices
• zero matrix
• addition of matrices
• the additive inverse of a matrix
• associative law for matrix addition
• subtraction of matrices
• multiplication of a matrix by a scalar
• multiplication of matrices
• left distribution for matrices
• right distribution for matrices
• transpose of a matrix
• periodic matrix
• idempotent matrix
• nilpotent matrix
• involutory matrix
• symmetric matrix
• skew-symmetric matrix
• hermitian matrix
• partitioning of a matrix
• identically partitions
• zero matrix
• inverse of a matrix
• properties of inverse of a matrix
• invertible matrix
• elementary row operations
• non-singular matrix
• row equivalent
• pivot column
• reduced echelon form
• row leader
• notation
• every elementary matrix is non-singular
• elementary column operations
• column equivalent
• rank of a matrix

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