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:
“The skyscraper establishes the block, the block creates the street, the street offers itself to man.”
—Roland Barthes (1915–1980)
“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)