Linked from

The 13 pages that link to Gram matrix, each with the reason it gives.

• Euclidean spaceRelated: It records lengths and angles for a chosen collection of Euclidean directions.

• Cauchy–Schwarz inequalityBroader topic: Its two-vector case has nonnegative determinant exactly because of this inequality.

• Dot productBroader topic: Its entries collect dot products to encode lengths, angles, and linear dependence.

• Linear independenceRelated: Its nonsingularity provides an independence test in inner-product spaces.

• Inner product spaceBroader topic: Its entries record the geometry of any chosen finite collection of vectors.

• Distance geometryRelated: Centering a squared distance matrix can recover the point configuration's Gram matrix.

• Bilinear formRelated: The matrix records the form's values on a chosen list of vectors.

• Bessel's inequalityRelated: Its positive semidefiniteness gives a finite-dimensional algebraic route to the inequality.

• Binet–Cauchy identityRelated: Applied to a matrix and its transpose, the identity yields sums of squared maximal minors.

• Bochner's theoremRelated: Positive definiteness requires every finite matrix of sampled function values to be positive semidefinite.

• Cauchy–Binet formulaRelated: Applying the formula to a matrix and its transpose yields its Gram determinant.

• De Gua's theoremRelated: Its minors encode squared areas, offering an algebraic route to the face-area relation.

• Pohlke's theoremRelated: It captures lengths and angles of spatial axes before projection changes their planar appearance.