# 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

### Lower Triangular Part of Symbolic Matrix

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]```

### Triangular Matrix On and Below Specified Superdiagonal

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]```

### Triangular Matrix On and Below Specified Subdiagonal

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]```

## Input Arguments

collapse all

Input, specified as a numeric or symbolic matrix.

Diagonal, specified as a numeric or symbolic number.