In mathematics, a block matrix or a partitioned matrix is a matrix which is interpreted as having been broken into sections called blocks. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines which break it out, or partition it, into a collection of smaller matrices.
This notion can be made more precise for an by matrix by partitioning into a collection, and then partitioning into a collection . The original matrix is then considered as the "total" of these groups, in the sense that the entry of the original matrix corresponds in a 1-to-1 and onto way to some offset entry of some, where and .
Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how the rows and columns of are partitioned.
Read more about Block Matrix: Example, Block Matrix Multiplication, Block Diagonal Matrices, Block Tridiagonal Matrices, Block Toeplitz Matrices, Direct Sum, Direct Product, Application
Famous quotes containing the words block and/or matrix:
“It is, in both cases, that a spiritual life has been imparted to nature; that the solid seeming block of matter has been pervaded and dissolved by a thought; that this feeble human being has penetrated the vast masses of nature with an informing soul, and recognised itself in their harmony, that is, seized their law. In physics, when this is attained, the memory disburthens itself of its cumbrous catalogues of particulars, and carries centuries of observation in a single formula.”
—Ralph Waldo Emerson (1803–1882)
“In all cultures, the family imprints its members with selfhood. Human experience of identity has two elements; a sense of belonging and a sense of being separate. The laboratory in which these ingredients are mixed and dispensed is the family, the matrix of identity.”
—Salvador Minuchin (20th century)