matrix algebra


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Related to matrix algebra: matrix multiplication

matrix algebra

[′mā·triks ′al·jə·brə]
(mathematics)
An algebra whose elements are matrices and whose operations are addition and multiplication of matrices.
References in periodicals archive ?
Upper triangular matrix algebras, block upper triangular matrix algebras, and nest algebras over a Hilbert space H are important examples of triangular algebras.
Solving the four simultaneous equations by hand is relatively easy, but as the number of departments grows, it's convenient to use matrix algebra and a computer to find the solution.
(1) [??] (2) This follows by Transfer of the result that an ordinary finite dimensional [C.sup.*]-algebra is isomorphic to a finite direct sum of internal matrix algebras of finite dimension over C.
Markov chains use matrix algebra methods to fore cast outcomes (states), given a starting point and probabilities that describe the chance of transitioning from one state to another state.
It is a nice illustration of a utilization of matrices in geometry, application of homogeneous coordinates, homogeneous transformation matrices and matrix algebra (Many similar exercises can be found in [Cox, 1998], [Craig, 1986], [Tsai, 1999]).
This book requires a good understanding of analysis of variance but not advanced linear model theory or matrix algebra. There are many symbols, many equations, and some algebra, but the concepts are well explained.
Somehow, viewing the methods of matrix algebra or calculus as bookkeeping devices makes the math much more palatable.
For example, students learn about normal distribution and standard deviation, regression and curve fitting, and matrix algebra for both equation solving and geometric transformations - areas of mathematics that most high school students never see.
is still a trace, and hence is a multiple of the unique trace on that matrix algebra. Thus to understand the trace in terms of the Bratteli diagram it is just necessary to know the normalization on each simple component.
Derive's math repertoire includes numerical and symbolic algebra, exact and approximate arithmetic, calculus, trigonometry, and matrix algebra. It can even calculate sophisticated functions, such as Bessel, Airy, zeta, and hypergeometric functions.
PC Macsyma performs basic and matrix algebra and trigonometry, differential and integral calculus, and vector and tensor analysis.