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.
Matrix Algebra and Discrete Mathematics THE CONSTRUCTION OF A NATIONAL TEST
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.
PC Macsyma performs basic and
matrix algebra and trigonometry, differential and integral calculus, and vector and tensor analysis.