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A matrix having a single row is called a row matrix. e. g. [1 3 5 7]
An m x n matrix A is said to be a square matrix if m = n i.e. number of rows = number of columns.
- The diagonal from left hand side upper corner to right hand side lower side lower corner is known as leading diagonal or principal diagonal. In the above example square matrix containing the elements 1, 3, 5 is called the leading or principal diagonal.
A square matrix all of whose elements except those in the leading diagonal, are zero is called a diagonal matrix. For a square matrix A = [aij]nxn to be a diagonal matrix, aij = 0, whenever i not equal to j.
A diagonal matrix whose all the leading diagonal elements are equal is called a scalar matrix.
A square matrix in which all the elements below the diagonal elements are zero is called Upper Triangular matrix and a square matrix in which all the elements above diagonal elements are zero is called Lower Triangular matrix.
Given a square matrix A = [aij]n´n,
For upper triangular matrix, aij = 0, i > j
and for lower triangular matrix, aij = 0, i < j
- Diagonal matrix is both upper and lower triangular
- A triangular matrix A = [aij]n´n is called strictly triangular if aii = 0 for 1 ≤ i ≤ n.