# triu

Return upper triangular part of symbolic matrix

## Syntax

``triu(A)``
``triu(A,k)``

## Description

````triu(A)` returns a triangular matrix that retains the upper part of the matrix `A`. The lower triangle of the resulting matrix is padded with zeros.```
````triu(A,k)` returns a matrix that retains the elements of `A` on and above the `k`-th diagonal. The elements below 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

### Upper Triangular Part of Symbolic Matrix

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

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

### Triangular Matrix On and Above Specified Superdiagonal

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

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

### Triangular Matrix On and Above Specified Subdiagonal

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

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

## Input Arguments

collapse all

Input, specified as a numeric or symbolic matrix.

Diagonal, specified as a numeric or symbolic number.