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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. [1] [2]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.
Loop tiling partitions a loop's iteration space into smaller chunks or blocks, so as to help ensure data used in a loop stays in the cache until it is reused. The partitioning of loop iteration space leads to partitioning of a large array into smaller blocks, thus fitting accessed array elements into cache size, enhancing cache reuse and eliminating cache size requirements.
The matrix includes one row for each subset in S and one column for each element in X. The entry in a particular row and column is 1 if the corresponding subset contains the corresponding element, and is 0 otherwise. In the matrix representation, an exact cover is a selection of rows such that each column contains a 1 in exactly one selected row.
Synonym for kernel-Hermitian matrices. Examples include (but not limited) to Hermitian, skew-Hermitian matrices, and normal matrices. Partitioned matrix: A matrix partitioned into sub-matrices, or equivalently, a matrix whose entries are themselves matrices rather than scalars. Synonym for block matrix. Parisi matrix: A block-hierarchical matrix.
An example of a recursive binary space partitioning quadtree for a 2D index.. Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies one or more requirements.
For example, consider the result if we were to union a checkerboard (where every tile is a pixel) of size with its complement. The result is a giant black square which should be represented by a quadtree with just the root node (coloured black), but instead the algorithm produces a full 4-ary tree of depth k {\displaystyle k} .
Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set or an ordered partition of a set,