Block matrix pseudoinverse information

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

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

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

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

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

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

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

Moore–Penrose pseudoinverse A + {\displaystyle A^{+}} is circulant. The matrix U {\displaystyle U} that is composed of the eigenvectors of a circulant matrix is...

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

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...

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

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...

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

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

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...

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

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

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

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...

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...

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

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...