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Regular Matrix (other)
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Regular matrix may refer to: Mathematics * Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive * The opposite of irregular matrix, a matrix with a different number of entries in each row * Regular Hadamard matrix, a Hadamard matrix whose row and column sums are all equal * A regular element of a Lie algebra, when the Lie algebra is ''gln'' * Invertible matrix (this usage is rare) Other uses * QS Regular Matrix, a quadraphonic sound system developed by Sansui Electric was a Japanese manufacturer of audio and video equipment. Headquartered in Tokyo, Japan, it was part of the Bermuda conglomerate (from 2011). The company was founded in Tokyo in 1947 by Kosaku Kikuchi, who had worked for a radio parts dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Matrix
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, ''substitution matrix'', or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics. There are several different definitions and types of stochastic matrices: *A right stochastic matrix is a square matrix of nonnegative real numbers, with each row summing to 1 (so it is also called a row stochastic matrix). *A left stochastic matrix is a square matrix of nonnegative real numbers, with each column summing to 1 (so it is also called a column stochastic matrix). *A ''doubly stochastic matrix'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irregular Matrix
An irregular matrix, or ragged matrix, is a matrix that has a different number of elements in each row. Ragged matrices are not used in linear algebra, since standard matrix transformations cannot be performed on them, but they are useful in computing as arrays which are called jagged arrays. Irregular matrices are typically stored using Iliffe vectors. For example, the following is an irregular matrix: : \begin 1 & 31 & 12& -3 \\ 7 & 2 \\ 1 & 2 & 2 \end See also * Regular matrix (other) * Empty matrix * Sparse matrix References * Paul E. BlackRagged matrix from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ..., 2004. Arrays Matrices (mathematics) {{matrix-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Hadamard Matrix
In mathematics a regular Hadamard matrix is a Hadamard matrix whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order must be a square number. The excess, denoted ''E''(''H''), of a Hadamard matrix ''H'' of order ''n'' is defined to be the sum of the entries of ''H''. The excess satisfies the bound , ''E''(''H''), ≤ ''n''3/2. A Hadamard matrix attains this bound if and only if it is regular. Parameters If ''n'' = 4''u''2 is the order of a regular Hadamard matrix, then the excess is ±8''u''3 and the row and column sums all equal ±2''u''. It follows that each row has 2''u''2 ± ''u'' positive entries and 2''u''2 ∓ ''u'' negative entries. The orthogonality of rows implies that any two distinct rows have exactly ''u''2 ± ''u'' positive entries in common. If ''H'' is interpreted as the incidence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Element Of A Lie Algebra
In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible. For example, in a complex semisimple Lie algebra, an element X \in \mathfrak is regular if its centralizer in \mathfrak has dimension equal to the rank of \mathfrak, which in turn equals the dimension of some Cartan subalgebra \mathfrak (note that in earlier papers, an element of a complex semisimple Lie algebra was termed regular if it is semisimple and the kernel of its adjoint representation is a Cartan subalgebra). An element g \in G a Lie group is regular if its centralizer has dimension equal to the rank of G . Basic case In the specific case of \mathfrak_n(\mathbb), the Lie algebra of n \times n matrices over an algebraically closed field \mathbb (such as the complex numbers), a regular element M is an element whose Jordan normal form contains a single Jordan block for each eigenvalue (in other words, the geometric multiplicity of each eigen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invertible Matrix
In linear algebra, an invertible matrix (''non-singular'', ''non-degenarate'' or ''regular'') is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their inverse. Definition An -by- square matrix is called invertible if there exists an -by- square matrix such that\mathbf = \mathbf = \mathbf_n ,where denotes the -by- identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix is uniquely determined by , and is called the (multiplicative) ''inverse'' of , denoted by . Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. Over a field, a square matrix that is ''not'' invertible is called singular or deg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
QS Regular Matrix
Quadraphonic Sound (originally called Quadphonic Synthesizer, and later incorrectly referred to as RM or Regular Matrix) was a phase amplitude Matrix decoder, matrix 4-channel quadraphonic sound system for phonograph records. The system was based on technology created by Peter Scheiber, but further developed by engineer Ryosuke Ito of Sansui Electric, Sansui in the early 1970s. The technology was freely licensed and was adopted by many record labels including ABC Records, ABC, Advent, BluesWay Records, BluesWay, Candide, Command Records, Command, Decca Records, Decca, Impulse! Records, Impulse, Longines Symphonette Society, Longines, MCA Records, MCA, Passport Records, Passport, Pye Records, Pye, Turnabout and Vox Records, Vox. More than 600 LP record titles using this technology were released on vinyl during the 1970s. RM (''Regular Matrix'') was often used a synonym for the 'Sansui QS', 'Toshiba QM' and 'Nippon Columbia QX' matrix systems that were previously launched before the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
