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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.
In statistical mechanics, the softargmax function is known as the Boltzmann distribution (or Gibbs distribution): [5]: 7 the index set , …, are the microstates of the system; the inputs are the energies of that state; the denominator is known as the partition function, often denoted by Z; and the factor β is called the coldness (or ...
Synonym for (0,1)-matrix or logical matrix. [1] Bisymmetric matrix: A square matrix that is symmetric with respect to its main diagonal and its main cross-diagonal. Block-diagonal matrix: A block matrix with entries only on the diagonal. Block matrix: A matrix partitioned in sub-matrices called blocks. Block tridiagonal matrix
The transfer-matrix method is used when the total system can be broken into a sequence of subsystems that interact only with adjacent subsystems. For example, a three-dimensional cubical lattice of spins in an Ising model can be decomposed into a sequence of two-dimensional planar lattices of spins that interact only adjacently.
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.
As compared to regression analysis, which creates a formula that health care providers can use to calculate the probability that a patient has a disease, recursive partition creates a rule such as 'If a patient has finding x, y, or z they probably have disease q'. A variation is 'Cox linear recursive partitioning'. [2]
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.
The iterative proportional fitting procedure (IPF or IPFP, also known as biproportional fitting or biproportion in statistics or economics (input-output analysis, etc.), RAS algorithm [1] in economics, raking in survey statistics, and matrix scaling in computer science) is the operation of finding the fitted matrix which is the closest to an initial matrix but with the row and column totals of ...