Matrices

Some articles on matrices:

Sparse Vector - Band Matrix
... An important special type of sparse matrices is band matrix, defined as follows ... Notice that zeros are represented with dots Matrices with reasonably small upper and lower bandwidth are known as band matrices and often lend themselves to simpler algorithms than general ...
Capelli's Identity - Contents
3 Generalizations 3.1 Turnbull's identity for symmetric matrices 3.2 The Howe–Umeda–Kostant–Sahi identity for antisymmetric matrices 3.3 The Caracciolo–Sportiello–Sokal ...
Matrix (mathematics) - History
... Matrices have a long history of application in solving linear equations ... emphasized determinants more strongly than matrices and an independent matrix concept akin to the modern notion emerged only in 1858, with Cayley's Memoir on the theory of matrices ... today called minors, that is to say, determinants of smaller matrices that derive from the original one by removing columns and rows ...
Capelli's Identity - Statement
... Eij can be written in a matrix form where are matrices with elements Eij, xij, respectively ... If all elements in these matrices would be commutative then clearly ... For generic noncommutative matrices formulas like do not exist, and the notion of the 'determinant' itself does not make sense for generic ...