# sqrtm() Function & Examples

Use the sqrtm() arithmetic function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## sqrtm

#### sqrtm(x)

Try it yourself:

```calculio
sqrtm([[33, 24], [48, 57]])
```

[sqrt](https://calcul.io/function/sqrt/index.md)

[abs](https://calcul.io/function/abs/index.md)

[square](https://calcul.io/function/square/index.md)

[multiply](https://calcul.io/function/multiply/index.md)

---

## sqrtm(): Matrix Square Root

**sqrtm()** computes a matrix B whose product B×B equals the input matrix. It is used in covariance transformations, control theory, and advanced linear algebra.

## Matrix, not entry-wise root

sqrtm differs from applying [sqrt()](https://calcul.io/function/sqrt/index.md) to entries. Results can be complex and may not be unique. Verify a candidate by [multiply()](https://calcul.io/function/multiply/index.md)ing it by itself, and inspect shape with [size()](https://calcul.io/function/size/index.md).

For symmetric positive-definite matrices, decompositions such as [lu()](https://calcul.io/function/lu/index.md) or [qr()](https://calcul.io/function/qr/index.md) may be useful depending on the task. Account for numerical error when checking equality.

[All functions](https://calcul.io/functions/index.md)