solved the matrix equation Ax = b, for matrix A with given vector b, using an LU factorization of A, where A = LU, [L b] = [I y], and [U y] = [I x]. LU factorizations are very common in business and industry, used for data analysis. This problem is from chapter 2.5 in David C. Lay's textbook, "Linear Algebra and it's Applications," 3rd Edition, currently used at UCSD. This is pic. 2 of 4 pics.
I spent 3.5 years in a library reading and solving math problems contained within several math textbooks, such as intro. to elem. linear algebra w/ applications, discrete mathematics with applications, linear algebra; applications version by Anton and Rorres, while also studying two linear algebra textbooks I bought at Barnes and Noble with more advanced treatments that include problems above linear 500 college level problems.
My first exposure to linear algebra came from a class I was required to take for my major, BSEE at George Mason University, Fairfax, where we used the textbook with the title, Introduction to Elementary Linear Algebra with Applications required for all students in engineering majors - to graduate.
I completed a more advanced treatment of linear algebra textbook, Linear Algebra; Schaum's Outline, Sixth Edition, that covers advanced physics and advanced engineering with diagonalization, minimal polynomial tests, linear functionals and the dual space, bilinear forms, quadratic forms, Hermitian forms, and more.
I recently bought 3 advanced math textbooks (graduate level-linear algebra and its applications, theoretical linear algebra, and ordinary differential equations) that cover advanced physics, including quantum physics, and also with applications in advanced engineering including the math for spectral theory, and spectral applications, special relativity problems, and minimal polynomial tests used in problems contained within quantitative analysis. I have already solved a minimal polynomial problem where I will be posting the complete hand written solution on Facebook, Instagram, Twitter, and a web page from photographs of it. -Mark R. Rowe
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