Concepts inThe computation of elementary unitary matrices
LAPACK
LAPACK (Linear Algebra PACKage) is a software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008).
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Identity matrix
In linear algebra, the identity matrix or unit matrix of size n is the n×n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.
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Unitary matrix
In mathematics, a unitary matrix is a (square) complex matrix satisfying the condition \t \t where is the identity matrix in n dimensions and is the conjugate transpose (also called the Hermitian adjoint) of . This condition implies that a matrix is unitary if and only if it has an inverse which is equal to its conjugate transpose A unitary matrix in which all entries are real is an orthogonal matrix.
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Column vector
In linear algebra, a column vector or column matrix is an m × 1 matrix, i.e. a matrix consisting of a single column of m elements. The transpose of a column vector is a row vector and vice versa. The set of all column vectors with a given number of elements forms a vector space which is the dual space to the set of all row vectors with that number of elements.
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Subroutine
In computer science, a subroutine, also termed procedure, function, routine, method, or subprogram, is a part of source code within a larger computer program that performs a specific task and is relatively independent of the remaining code. As the name subprogram suggests, a subroutine behaves in much the same way as a computer program that is used as one step in a larger program or another subprogram.
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Vector space
A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
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E (verification language)
e is a hardware verification language (HVL) which is tailored to implementing highly flexible and reusable verification testbenches.
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