Determinants | Analytic geometry | Matrices

Gram matrix

In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors in an inner product space is the Hermitian matrix of inner products, whose entries are given by the inner product . If the vectors are the columns of matrix then the Gram matrix is in the general case that the vector coordinates are complex numbers, which simplifies to for the case that the vector coordinates are real numbers. An important application is to compute linear independence: a set of vectors are linearly independent if and only if the (the determinant of the Gram matrix) is non-zero. It is named after Jørgen Pedersen Gram. (Wikipedia).

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From playlist Linear Algebra for Computer Scientists

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From playlist Intro to Matrices

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From playlist Introducing linear algebra

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From playlist MIT 18.06 Linear Algebra, Spring 2005

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From playlist Orthogonal and Orthonormal Sets of Vectors

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From playlist Augmented Matrices

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Related pages

Rotation matrix | Linear span | Jørgen Pedersen Gram | Mercer's theorem | Vector space | Linear algebra | Hermitian matrix | Orthogonal transformation | Dot product | Linear independence | Covariance matrix | Determinant | Conjugate transpose | Singular value decomposition | Controllability Gramian | Riemannian geometry | Simplex | Square-integrable function | Kernel principal component analysis | Square root of a matrix | Cholesky decomposition | Control theory | Unitary transformation | Field (mathematics) | Orthonormal basis | Parallelepiped | Symmetric matrix | Observability Gramian | Unitary matrix | Complex conjugate | Bilinear form | Systems theory | Orthogonal matrix | Random variable | Complex number | Finite element method | Transpose | Inner product space | Exterior product