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Although an explicit inverse is not necessary to estimate the vector of unknowns, it is the easiest way to estimate their accuracy, found in the diagonal of a matrix inverse (the posterior covariance matrix of the vector of unknowns). However, faster algorithms to compute only the diagonal entries of a matrix inverse are known in many cases. [19]
4. Every network matrix is TU. The rows of a network matrix correspond to a tree T = (V, R), each of whose arcs has an arbitrary orientation (it is not necessary that there exist a root vertex r such that the tree is "rooted into r" or "out of r").The columns correspond to another set C of arcs on the same vertex set V.
In mathematics, a jacket matrix is a square symmetric matrix = of order n if its entries are non-zero and real, complex, or from a finite field, and Hierarchy of matrix types A B = B A = I n {\displaystyle \ AB=BA=I_{n}}
A square matrix having a multiplicative inverse, that is, a matrix B such that AB = BA = I. Invertible matrices form the general linear group. Involutory matrix: A square matrix which is its own inverse, i.e., AA = I. Signature matrices, Householder matrices (Also known as 'reflection matrices' to reflect a point about a plane or line) have ...
The nodes in the first tree are univariate random variables. The edges are constraints or conditional constraints explained as follows. Recall that an edge in a tree is an unordered set of two nodes. Each edge in a vine is associated with a constraint set, being the set of variables (nodes in first tree) reachable by the set membership relation ...
The local inverse is a kind of inverse function or matrix inverse used in image and signal processing, as well as in other general areas of mathematics. The concept of a local inverse came from interior reconstruction of CT [clarification needed] images. One interior reconstruction method first approximately reconstructs the image outside the ...
Any real symplectic matrix can be decomposed as a product of three matrices: = ′, where and ′ are both symplectic and orthogonal, and is positive-definite and diagonal. [6] This decomposition is closely related to the singular value decomposition of a matrix and is known as an 'Euler' or 'Bloch-Messiah' decomposition.
This can be seen by applying in turn each of the unimodular inverse matrices A −1, B −1, and C −1 to an arbitrary primitive Pythagorean triple (d, e, f), noting that by the above reasoning primitivity and the Pythagorean property are retained, and noting that for any triple larger than (3, 4, 5) exactly one of the inverse transition ...