Matrices Overview and Types

Matrices

• A matrix is a rectangular arrangement of numbers enclosed in brackets.
• Each number in a matrix is an element.
• An m x n matrix has m rows and n columns.

Types of Matrices

• A square matrix has the same number of rows and columns.
• A column matrix has one column.
• A row matrix has one row.
• A vector is a matrix with one row or one column.
• A zero matrix has all elements equal to zero.
• A diagonal matrix is a square matrix with non-diagonal elements equal to zero.
• An identity matrix is a diagonal matrix with all diagonal elements equal to 1.
• A scalar matrix is a square matrix with a constant value on the diagonal and zeros elsewhere.

Position of Elements

• Elements are identified by their row and column, denoted using double subscript notation.
• a_ij represents the element in row i and column j.
• The principal diagonal consists of elements a_ii where i is the row and column number.

Transpose

• The transpose of a matrix A is denoted A^T.
• It is created by swapping the rows and columns of the original matrix.
• If the original matrix is m x n, the transpose is n x m.