16 topics

Linear algebra

Vectors, matrices, eigenvalues and projections: the algebra behind machine learning.

Chat with the Linear algebra assistantStart with: Eigenvalues and eigenvectors, Dot product, Least squares

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Basis and spanThe span of vectors contains all their linear combinations. A basis is an independent set that spans a vector space.

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Condition numberA condition number measures how sensitive a problem solution is to input perturbations. It describes the problem, distinct from…

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Eigenvalues and eigenvectorsAn eigenvector is a nonzero vector whose direction is preserved by a square linear map. Its eigenvalue is the corresponding scaling factor.

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Null spaceThe null space of A is the set of vectors mapped to zero by A. It is a subspace of the input space.

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Orthogonal projectionOrthogonal projection finds the closest vector in a subspace under the Euclidean norm. The residual is perpendicular to that subspace.

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Singular value decompositionSVD factors a real matrix into orthogonal directions, nonnegative scale factors, and another orthogonal change of coordinates. It applies…

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