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A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

A Redheffer matrix is a square (0,1)-matrix with elements a_(ij) equal to 1 if j=1 or i|j (i divides j), and 0 otherwise. For n=1, 2, ..., the first few Redheffer matrices ...

A square n×n matrix A=a_(ij) is called reducible if the indices 1, 2, ..., n can be divided into two disjoint nonempty sets i_1, i_2, ..., i_mu and j_1, j_2, ..., j_nu (with ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees module of M with respect to F is ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...