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The simplest rectilinear polygon is an axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle . A golygon is a rectilinear polygon whose side lengths in sequence are consecutive integers.
The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices. QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column.
Polygon decomposition is applied in several areas: [1] Pattern recognition techniques extract information from an object in order to describe, identify or classify it. An established strategy for recognising a general polygonal object is to decompose it into simpler components, then identify the components and their interrelationships and use this information to determine the shape of the object.
Decomposition: This is a version of Schur decomposition where and only contain real numbers. One can always write A = V S V T {\displaystyle A=VSV^{\mathsf {T}}} where V is a real orthogonal matrix , V T {\displaystyle V^{\mathsf {T}}} is the transpose of V , and S is a block upper triangular matrix called the real Schur form .
The Cauchy–Binet formula is a generalization of that product formula for rectangular matrices. This formula can also be ... For example, LU decomposition ...
Specifically, the singular value decomposition of an complex matrix is a factorization of the form =, where is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, is an complex unitary matrix, and is the conjugate transpose of . Such decomposition ...
The decomposition can be derived from the fundamental property of eigenvectors: = = =. The linearly independent eigenvectors q i with nonzero eigenvalues form a basis (not necessarily orthonormal) for all possible products Ax, for x ∈ C n, which is the same as the image (or range) of the corresponding matrix transformation, and also the ...
The pseudoinverse is defined for all rectangular matrices whose entries are real or complex numbers. Given a rectangular matrix with real or complex entries, its pseudoinverse is unique. It can be computed using the singular value decomposition.