# The language of matrices

## The language of matrices

## Basics of Matrices

- In general, a
**matrix**is a rectangular array of numbers. - The order of a matrix is given by the number of rows and columns it has. A
**2x3 matrix**has 2 rows and 3 columns. - A
**vector**can be regarded as a matrix with only one column or one row. - A
**square matrix**is a matrix where the number of rows is equal to the number of columns. - The numbers in a matrix are commonly referred to as
**elements or entries**.

## Types of Matrices

**Row matrix**: Matrix with a single row.**Column matrix**: Matrix with a single column.**Zero or Null Matrix**: All elements in the matrix are zero.**Diagonal Matrix**: Elements outside the main diagonal are zero.**Scalar Matrix**: All non-diagonal elements are zero and all diagonal elements are same.**Unity or Identity Matrix**: All diagonal elements are one and non-diagonal elements are zero.

## Operations on Matrices

**Addition and Subtraction**: Same order matrices can be added or subtracted element by element.**Scalar Multiplication**: Every element of matrix can be multiplied by a scalar.**Matrix Multiplication**: The number of columns in the first matrix should be equal to the number of rows in the second matrix for multiplication. The multiplying process refers to the dot product.**Transpose of a Matrix**: Transpose of a matrix is a new matrix whose rows are the columns of the original.

## Special Terms in Matrix

**Main Diagonal**: In a square matrix, the main diagonal (or principal diagonal) is the set of elements running from the top left corner to the bottom right.**Determinant**: A special numerical value calculated from a square matrix.**Minor and Cofactor**: For each element in the matrix, there is a corresponding minor and cofactor derived based on determinant of sub-matrix.**Inverse of a matrix**: Only square matrices have inverses. The matrix when multiplied by its inverse results in identity matrix. An inverse matrix does not exist if determinant is zero (matrix is called singular).**Rank of a matrix**: The maximum number of linearly independent rows in a matrix.