partitioned matrix
A partitioned matrix, or a block matrix, is a matrix that has been constructed from other smaller matrices. These smaller matrices are called blocks or sub-matrices of .
and write as
If are square matrices (of possibly different sizes), then we define the direct sum of the matrices as the partitioned matrix
where the off-diagonal blocks are zero.
If and are matrices of the same size partitioned into blocks of the same size, the partition of the sum is the sum of the partitions.
If and are and matrices, respectively, then if the blocks of and are of the correct size to be multiplied, then the blocks of the product are the products of the blocks.
Title | partitioned matrix |
---|---|
Canonical name | PartitionedMatrix |
Date of creation | 2013-03-22 13:32:55 |
Last modified on | 2013-03-22 13:32:55 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 11 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 15-00 |
Related topic | JordanCanonicalForm |
Related topic | JordanCanonicalFormTheorem |
Defines | block matrix |
Defines | sub-matrix |
Defines | submatrix |