We designed and implemented a simple and utilitarian C# matrix class for double precision numbers. The class has the binary matrix operators +, -, *, / which are addition, subtraction, multiplication, and division of two matrices. We also include an operator for multiplication of matrix by a scalar and an operator for dividing a matrix by a scalar. We have included functions to compute the p-norm, p, q-norm, and max norm of a matrix. We also can calculate using truncated infinite series the exponential, cosine, and sine function of a matrix. The exponential and trigonometric functions use a powering function that raises a matrix to a non-negative integral power.
Below is a screenshot of the test Windows Forms application. We execute the four binary matrix operators in the order +, -, *, / e.g. A+B, A-B, A*B, A/B. In order to divide by B, the matrix B must be square and non-singular, that is square and invertible.
The B matrix has the form of the matrix in the online discussion:
http://www.purplemath.com/modules/mtrxinvr2.htm
We create a project named MatrixExample. In this project we add a Matrix class whose code is given below:
Matrix
I leave it as an exercise for the reader to test the various norms and other functions.
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
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Numerical Explorations 