# svd() Function & Examples

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

Try it yourself:

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## svd(): singular value decomposition

**svd(A)** decomposes a matrix into orthogonal factors and singular values. It exposes rank, dominant directions, and numerical conditioning.

## What it provides

Conceptually, SVD writes A as U × S × Vᵀ. The diagonal singular values show how strongly the matrix acts along independent directions. Small values can signal near-dependence in data.

## Applications

Use SVD for dimensionality reduction, least-squares fitting, and low-rank approximation. Related tools include [pinv()](https://calcul.io/function/pinv/index.md), [transpose()](https://calcul.io/function/transpose/index.md), [multiply()](https://calcul.io/function/multiply/index.md), [qr()](https://calcul.io/function/qr/index.md), and [det()](https://calcul.io/function/det/index.md).

## Caveat

SVD is computationally expensive for large matrices. Choose a tolerance deliberately when deciding which singular values count as zero.

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