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In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication.This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group.
set is smaller than its power set; uncountability of the real numbers; Cantor's first uncountability proof. uncountability of the real numbers; Combinatorics; Combinatory logic; Co-NP; Coset; Countable. countability of a subset of a countable set (to do) Angle of parallelism; Galois group. Fundamental theorem of Galois theory (to do) Gödel number
The unitary group is a subgroup of the general linear group GL(n, C), and it has as a subgroup the special unitary group, consisting of those unitary matrices with determinant 1. In the simple case n = 1, the group U(1) corresponds to the circle group, isomorphic to the set of all complex numbers that have absolute value 1, under multiplication ...
In mathematics, Schur's lemma [1] is an elementary but extremely useful statement in representation theory of groups and algebras.In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0.
For a linear algebraic group G over the real numbers R, the group of real points G(R) is a Lie group, essentially because real polynomials, which describe the multiplication on G, are smooth functions. Likewise, for a linear algebraic group G over C, G(C) is a complex Lie group. Much of the theory of algebraic groups was developed by analogy ...
In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in terms of the norm. The ...
In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916). It is often used to derive binomial identities, most notably Dixon's identity.
P. Oxy. 29, one of the oldest surviving fragments of Euclid's Elements, a textbook used for millennia to teach proof-writing techniques. The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the
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