tril

Return lower triangular part of symbolic matrix

Syntax

`tril(A)tril(A,k)`

Description

`tril(A)` returns a triangular matrix that retains the lower part of the matrix `A`. The upper triangle of the resulting matrix is padded with zeros.

`tril(A,k)` returns a matrix that retains the elements of `A` on and below the `k`-th diagonal. The elements above the `k`-th diagonal equal to zero. The values ```k = 0```, `k > 0`, and `k < 0` correspond to the main, superdiagonals, and subdiagonals, respectively.

Examples

Display the matrix retaining only the lower triangle of the original symbolic matrix:

```syms a b c A = [a b c; 1 2 3; a + 1 b + 2 c + 3]; tril(A)```
```ans = [ a, 0, 0] [ 1, 2, 0] [ a + 1, b + 2, c + 3]```

Display the matrix that retains the elements of the original symbolic matrix on and below the first superdiagonal:

```syms a b c A = [a b c; 1 2 3; a + 1 b + 2 c + 3]; tril(A, 1)```
```ans = [ a, b, 0] [ 1, 2, 3] [ a + 1, b + 2, c + 3]```

Display the matrix that retains the elements of the original symbolic matrix on and below the first subdiagonal:

```syms a b c A = [a b c; 1 2 3; a + 1 b + 2 c + 3]; tril(A, -1)```
```ans = [ 0, 0, 0] [ 1, 0, 0] [ a + 1, b + 2, 0]```

Get trial now