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Block matrix. Matrix defined using smaller matrices called blocks. 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 ...
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.
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions.
In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or . [1] Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: Input: matrices A and B.
Pivot element. The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this ...
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...
Khatri–Rao product. In mathematics, the Khatri–Rao product or block Kronecker product of two partitioned matrices and is defined as [1][2][3] in which the ij -th block is the mipi × njqj sized Kronecker product of the corresponding blocks of A and B, assuming the number of row and column partitions of both matrices is equal.