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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(), transpose(), multiply(), qr(), and det().

Caveat

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

Try Svd in Calcul.io

Start with one of the editable examples above, then replace its arguments with your own values. Keeping the function on a separate calculator line makes the input and result easy to compare. For a longer workflow, assign the result to a variable or reference that line in the next expression.

Check the shown signature before adding optional arguments, and use the related-function links to compare operations with similar purposes.

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