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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.
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. It consist of growing blocks placed along the diagonal, each block is itself a Parisi matrix of a smaller size.
In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier .
The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for
partition of a matrix; see block matrix, and partition of the sum of squares in statistics problems, especially in the analysis of variance , quotition and partition , two ways of viewing the operation of division of integers.
Transfer-matrix method may refer to: Transfer-matrix method (statistical mechanics) , a mathematical technique used to write the partition function into a simpler form. Transfer-matrix method (optics) , a method to analyze the propagation of electromagnetic or acoustic waves through a stratified medium.
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.
Partition a matrix and its inverse in four submatrices: [] = []. The partition on the right-hand side should be the transpose of the partition on the left-hand side, in the sense that if A is an m-by-n block then E should be an n-by-m block.