In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating...

A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently...

on different state variables, e.g., miles versus kilometers. Block matrix pseudoinverse Regular semigroup Ben-Israel & Greville 2003, pp. 2, 7 Nakamura...

update to a determinant Invertible matrix Moore–Penrose pseudoinverse § Updating the pseudoinverse Max A. Woodbury, Inverting modified matrices, Memorandum...

cofactor matrix Conjugate transpose Converse relation Moore–Penrose pseudoinverse Projection (linear algebra) Nykamp, Duane. "The transpose of a matrix". Math...

theorem LU decomposition Matrix decomposition Matrix square root Minor (linear algebra) Partial inverse of a matrix Pseudoinverse Rybicki Press algorithm...

where K 11 + {\displaystyle K_{11}^{+}} is the Moore–Penrose pseudoinverse of K 11 {\displaystyle K_{11}} , which must exist since K 11 {\displaystyle...

circulant matrix, its Moore–Penrose pseudoinverse A + {\displaystyle A^{+}} is circulant. The discrete Fourier transform matrix of order n {\displaystyle n}...

matrix, singular value decomposition (SVD) is equally useful. With A factored as UΣVT, a satisfactory solution uses the Moore-Penrose pseudoinverse,...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

subspace Block matrix pseudoinverse Bidiagonalization Cuthill–McKee algorithm — permutes rows/columns in sparse matrix to yield a narrow band matrix In-place...

square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is...

in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the...

hold. Block matrix pseudoinverse Sylvester's law of inertia Haynsworth, E. V., "Determination of the inertia of a partitioned Hermitian matrix", Linear...

combinations of the others. Matrix exponential — defined by the exponential series. Matrix representation of conic sections Pseudoinverse — a generalization of...

matrix Jordan normal form Weyr canonical form Rank Matrix inversion, invertible matrix Pseudoinverse Adjugate Transpose Dot product Symmetric matrix Orthogonal...

{X} ^{+})^{*}=\mathbf {X} \mathbf {X} ^{+}} (the property of pseudoinverse), the matrix U P U T {\displaystyle UPU^{\rm {T}}} is an orthogonal projection...

|_{+}}}}={\frac {1}{\sqrt {|2\pi \mathbf {\Sigma } |_{+}}}}\,.} Matrix determinant Moore–Penrose pseudoinverse, which can also be obtained in terms of the non-zero...

P_{A}=AA^{+}} . Here A + {\displaystyle A^{+}} stands for the Moore–Penrose pseudoinverse. This is just one of many ways to construct the projection operator...

of a column vector, or a block of column vectors, by T = P − 1 {\displaystyle T=P^{-1}} , is commonly performed in a matrix-free fashion, i.e., where...

Jacobian matrix and determinant Joint constraints Kinematic synthesis Kinemation Levenberg–Marquardt algorithm Motion capture Physics engine Pseudoinverse Ragdoll...

\mathbf {M} ^{-1}\mathbf {Q} ),} where the '+' symbol denotes the pseudoinverse of the matrix A M − 1 / 2 {\displaystyle \mathbf {A} \mathbf {M} ^{-1/2}} ...

converge. However, due to the high complexity of the matrix-inversion operation, computing the pseudoinverse in high-dimensional cases is in many cases intractable...

A_{t,s}^{\dagger }} is the t , s {\displaystyle t,s} element of the pseudoinverse of A {\displaystyle A} , and H k {\displaystyle {\mathcal {H}}_{k}}...

equations is given in terms of the matrix ( A T A ) − 1 A T {\displaystyle (A^{T}A)^{-1}A^{T}} , called the pseudoinverse of A, by x ^ = ( A T A ) − 1 A T...

then the orthogonal matrix is replaced by a block matrix that is orthogonal in the nondegenerate block, and the diagonal matrix has zero-valued entries...

satellites for a solution, Bancroft uses the generalized inverse (i.e., the pseudoinverse) to find a solution. A case has been made that iterative methods, such...

a pseudo-division, by setting a/b = ab+, in which b+ represents the pseudoinverse of b. It can be proven that if b−1 exists, then b+ = b−1. If b equals...

is used to estimate the coefficient vector using the Moore–Penrose pseudoinverse: β ^ = ( X T X ) − 1 X T y {\displaystyle {\hat {\boldsymbol {\beta...