TYPES OF MATRIX

A matrix may be classified by types. It is possible for a matrix to belong to more than one type. A row matrix is a matrix with only one row. A column matrix is a matrix with only one column. A zero matrix or a null matrix is a matrix that has all its elements zero. A square matrix is a matrix with an equal number of rows and columns. A diagonal matrix is a square matrix that has all its elements zero except for those in the diagonal from top left to bottom right; which is known as the leading diagonal of the matrix. A scalar matrix is a diagonal matrix where all the diagonal elements are equal An upper triangular matrix is a square matrix where all the elements located below the diagonal are zeros A lower triangular matrix is a square matrix where all the elements located above the diagonal are zeros. A matrix which is upper as well as lower is called triangular matrix A unit matrix or identity matrix is a diagonal matrix whose elements in the diagonal are all ones. Transpose of a matrix. The matrix resulting from interchanging the rows and columns of matrix. Symmetric matrix. A square matrix in which corresponding elements with respect to the diagonal are equal; a matrix in which aij = aji where aij is the element in the i-th row and j-th column; a matrix which is equal to its transpose; a square matrix in which a flip about the diagonal leaves it unchanged. Skew-symmetric matrix. A square matrix in which corresponding elements with respect to the diagonal are negatives of each other; a matrix in which aij = -aji where aij is the element in the i-th row and j-th column; a matrix which is equal to the negative of its transpose. The diagonal elements are always zeros Periodic matrix. A matrix A for which Ak+1 = A , where k is a positive integer. If k is the least positive integer for which Ak+1 = A , then A is said to be of period k. Idempotent matrix if A2 = A, then A is called idempotent. Nilpotent matrix. A matrix A for which Ap = 0, where p is some positive integer. If p is the least positive integer for which Ap = 0, then A is said to be nilpotent of index p.