# istriu

Determine if matrix is upper triangular

## Syntax

• `tf = istriu(A)` example

## Description

example

````tf = istriu(A)` returns logical `1` (`true`) if `A` is an upper triangular matrix; otherwise, it returns logical `0` (`false`).```

## Examples

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### Test Upper Triangular Matrix

Create a 5-by-5 matrix.

`A = triu(magic(5))`
```A = 17 24 1 8 15 0 5 7 14 16 0 0 13 20 22 0 0 0 21 3 0 0 0 0 9```

Test `A` to see if it is upper triangular.

`istriu(A)`
```ans = 1 ```

The result is logical `1` (`true`) because all elements below the main diagonal are zero.

### Test Matrix of Zeros

Create a 5-by-5 matrix of zeros.

`Z = zeros(5);`

Test `Z` to see if it is upper triangular.

`istriu(Z)`
```ans = 1 ```

The result is logical `1` (`true`) because an upper triangular matrix can have any number of zeros on the main diagonal.

## Input Arguments

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### `A` — Input arraynumeric array

Input array, specified as a numeric array. `istriu` returns logical `0` (`false`) if `A` has more than two dimensions.

Data Types: `single` | `double`
Complex Number Support: Yes

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### Upper Triangular Matrix

A matrix is upper triangular if all elements below the main diagonal are zero. Any number of the elements on the main diagonal can also be zero.

For example, the matrix

$A=\left(\begin{array}{cccc}1& -1& -1& -1\\ 0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}1& -2& -2\\ 0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}1& -3\\ 0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0& \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}1\end{array}\right)$

is upper triangular. A diagonal matrix is both upper and lower triangular.

### Tips

• Use the `triu` function to produce upper triangular matrices for which `istriu` returns logical `1` (`true`).

• The functions `isdiag`, `istriu`, and `istril` are special cases of the function `isbanded`, which can perform all of the same tests with suitably defined upper and lower bandwidths. For example, ```istriu(A) == isbanded(A,0,size(A,2))```.