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Pages in category "Theorems in linear algebra" The following 24 pages are in this category, out of 24 total. This list may not reflect recent changes. C.
Dimension theorem for vector spaces. Hamel dimension; Examples of vector spaces; Linear map. Shear mapping or Galilean transformation; Squeeze mapping or Lorentz transformation; Linear subspace. Row and column spaces; Column space; Row space; Cyclic subspace; Null space, nullity; Rank–nullity theorem; Nullity theorem; Dual space. Linear ...
Exchange theorem (linear algebra) Gamas's Theorem (multilinear algebra) Gershgorin circle theorem (matrix theory) Inverse eigenvalues theorem (linear algebra) Perron–Frobenius theorem (matrix theory) Principal axis theorem (linear algebra) Rank–nullity theorem (linear algebra) Rouché–Capelli theorem (Linear algebra) Sinkhorn's theorem ...
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...
Theorems in linear algebra ... Theorems in abstract algebra (9 C, 23 P) Pages in category "Theorems in algebra" The following 32 pages are in this category, out of 32 ...
In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive procedure for finding them.
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz.