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# istril

Determine if matrix is lower triangular

## Description

example

tf = istril(A) returns logical 1 (true) if A is a lower triangular matrix; otherwise, it returns logical 0 (false).

## Examples

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### Test Lower Triangular Matrix

Create a 5-by-5 matrix.

`D = tril(magic(5))`
```D =

17     0     0     0     0
23     5     0     0     0
4     6    13     0     0
10    12    19    21     0
11    18    25     2     9```

Test D to see if it is lower triangular.

`istril(D)`
```ans =

1```

The result is logical 1 (true) because all elements above 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 lower triangular.

`istril(Z)`
```ans =

1```

The result is logical 1 (true) because a lower triangular matrix can have any number of zeros on its main diagonal.

## Input Arguments

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### A — Input arraynumeric array

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

Data Types: single | double
Complex Number Support: Yes

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### Lower Triangular Matrix

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

For example, the matrix

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

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

### Tips

• Use the tril function to produce lower triangular matrices for which istril 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, istril(A) == isbanded(A,size(A,1),0).