Category:Triangular Matrices
This category contains results about Triangular Matrices.
Definitions specific to this category can be found in Definitions/Triangular Matrices.
Let $\mathbf T = \begin {bmatrix} a_{1 1} & a_{1 2} & \cdots & a_{1 n} \\ a_{2 1} & a_{2 2} & \cdots & a_{2 n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m 1} & a_{m 2} & \cdots & a_{m n} \\ \end {bmatrix}$ be a matrix of order $m \times n$.
Then $\mathbf T$ is a triangular matrix if and only if all the elements either above or below the diagonal are zero.
Upper Triangular Matrix
An upper triangular matrix is a matrix in which all the lower triangular elements are zero.
That is, all the non-zero elements are on the main diagonal or in the upper triangle.
That is, $\mathbf U$ is upper triangular if and only if:
- $\forall a_{ij} \in \mathbf U: i > j \implies a_{ij} = 0$
Lower Triangular Matrix
A lower triangular matrix is a matrix in which all the upper triangular elements are zero.
That is, all the non-zero elements are on the main diagonal or in the lower triangle.
That is, $\mathbf L$ is lower triangular if and only if:
- $\forall a_{i j} \in \mathbf U: i < j \implies a_{i j} = 0$
Subcategories
This category has the following 3 subcategories, out of 3 total.
Pages in category "Triangular Matrices"
The following 10 pages are in this category, out of 10 total.