Singular values

Singular values are nonnegative square roots of eigenvalues of the conjugate-transpose product.

Different ways to understand it

No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video

Orthogonal complements
Vectors orthogonal to every vector of a subspace form its orthogonal complement.
Positive-definite matrices
A symmetric or Hermitian matrix is positive definite when its quadratic form is positive on nonzero vectors.
Quadratic forms
A quadratic form assigns a homogeneous degree-two scalar expression to a vector.
Singular value decomposition
Unitary or orthogonal factors and a rectangular diagonal factor describe any finite matrix.
Basis and dimension
A basis is a linearly independent spanning set; every vector has unique coordinates in that basis.