Here you will learn what is the upper triangular matrix definition with examples.
Let’s begin –
Upper Triangular Matrix
Definition :
A square matrix A = \([a_{ij}]\) is called an upper triangular matrix if \(a_{ij}\) = 0 for all i > j.
Thus, in an upper triangular matrix, all elements below the main diagonal are zero.
Also Read : Different Types of Matrices – Definitions and Examples
Examples :
1). \(\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{bmatrix}\) is a upper triangular matrix.
The order of above matrix is \(3 \times 3\).
2). \(\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}\) is a upper triangular matrix.
The order of above matrix is \(2 \times 2\).
3). \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 5 & 1 & 3 \\ 0 & 0 & 2 & 9 \\ 0 & 0 & 0 & 5 \end{bmatrix}\) is a upper triangular matrix.
The order of above matrix is \(4 \times 4\).
