All Linear Algebra and Matrix Theory

The rank-nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M

In linear algebra, the Cayley-Hamilton theorem (named after the

In linear algebra and functional analysis, a spectral theorem is

In matrix theory, the Perron-Frobenius theorem, proved in its

Theorem) may be used to bound the spectrum of a square matrix. It was first published by the Soviet mathematician

In linear algebra, Cramer's rule is an explicit formula for the

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix

The Steinitz exchange lemma is a theorem in linear algebra concerning bases, dimensionality of a vector

In mathematics, specifically linear algebra, the Cauchy-Binet formula, named after Augustin-Louis

Rouché-Capelli theorem is a theorem in linear algebra that determines the number of solutions of a

Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions

In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have

The Motzkin-Taussky theorem is a result from operator and matrix theory about the representation of a sum of two bounded

In mathematics, specifically linear algebra, the Woodbury matrix identity - named after Max

In geometry and linear algebra, a principal axis is a certain line in a Euclidean

gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after

is the k × k identity matrix. It is closely related to the matrix determinant lemma and its generalization. It

orthogonal transformation in an n-dimensional symmetric bilinear space can be described as the composition of at most