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An inner product space is a vector space together with an inner product on it. If the inner product defines a complete metric, then the inner product space is called a ...

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

A vector norm defined for a vector x=[x_1; x_2; |; x_n], with complex entries by |x|_infty=max_(i)|x_i|. The vector norm |x|_infty of the vector x is implemented in the ...

A vector norm defined for a vector x=[x_1; x_2; |; x_n], with complex entries by |x|_1=sum_(r=1)^n|x_r|. The L^1-norm |x|_1 of a vector x is implemented in the Wolfram ...

This is proven in Rademacher and Toeplitz (1957).

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

The mixtilinear circle is the circumcircle of the mixtilinear triangle, i.e., the triangle formed by the centers of the mixtilinear incircles. Neither its center not circle ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

The geometry of the Lie group consisting of real matrices of the form [1 x y; 0 1 z; 0 0 1], i.e., the Heisenberg group.

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...