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A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

An n×n-matrix A is said to be diagonalizable if it can be written on the form A=PDP^(-1), where D is a diagonal n×n matrix with the eigenvalues of A as its entries and P is a ...

A stochastic matrix, also called a probability matrix, probability transition matrix, transition matrix, substitution matrix, or Markov matrix, is matrix used to characterize ...

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension. The most common use of an ...

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...

An integer n is called a super unitary perfect number if sigma^*(sigma^*(n))=2n, where sigma^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... ...