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In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. 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 up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.

Attributes	Values
rdf:type	Thing
rdfs:label	Block matrix (en)
rdfs:comment	In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. 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 up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned. (en)
rdfs:seeAlso	Helmert–Wolf blocking Matrix addition
sameAs	Block matrix Block matrix
dbp:wikiPageUsesTemplate	dbt:= dbt:Anchor dbt:Cite_web dbt:Cn dbt:For dbt:Refimprove dbt:Reflist dbt:See_also dbt:Short_description dbt:Sup dbt:Matrix_classes dbt:Linear_algebra
Subject	Sparse matrices Matrices
Link from a Wikipage to an external page	http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-3-multiplication-and-inverse-matrices
thumbnail	wiki-commons:Special:FilePath/BlockMatrix168square.png?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Block_matrix?oldid=1056614655&ns=0
Wikipage page ID	457464 (xsd:integer)
page length (characters) of wiki page	21497 (xsd:nonNegativeInteger)
Wikipage revision ID	1056614655 (xsd:integer)
Link from a Wikipage to another Wikipage	Very Large Scale Integration Weinstein–Aronszajn identity Basis (linear algebra) Bijection Biproduct Block LU decomposition Sparse matrices Category (mathematics) Jordan normal form Matrices Direct sum of modules Domain of a function Main diagonal Offset (computer science) Zero matrix Linear algebra Linear map Square matrix Toeplitz matrix Tridiagonal matrix Tridiagonal matrix algorithm Commutative property Computational fluid dynamics Computer science Conformable matrix Einstein notation Partition of a set Endomorphism Schur complement Determinant Diagonal Diagonal matrix Hamming(7,4) Interpretation (logic) Invertible matrix Kronecker product LU decomposition Trace (linear algebra) Transpose Vector space Strassen algorithm Mathematics Matrix (mathematics) Matrix addition Matrix multiplication Range of a function
has abstract	In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. 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 up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned. 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 way with some offset entry of some , where and . Block matrix algebra arises in general from biproducts in categories of matrices. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Block_matrix
is Wikipage redirect of	Block matrices Block tridiagonal matrix Block-diagonal matrix Block diagonal Block diagonal matrix Partitioned matrix Matrix block Matrix partition
is Link from a Wikipage to another Wikipage of	Grothendieck–Katz p-curvature conjecture Local linearization method NAS Parallel Benchmarks Non-linear least squares Normal coordinates Nullity theorem 3D rotation group Affine group Algebraic K-theory Attractor network Band matrix Bargmann–Wigner equations Basic Linear Algebra Subprograms Benders decomposition Berezinian

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