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
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