Matrix Determinant with Graphs for Laplace's and Expansion Methods
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The Laplace’s theorem and Expansion method for evaluation of the determinant ,for a instance ,of the 4∙4 matrix , can be used further for any matrices ,having advantageously the higher rank than 3∙3 matrix. But necessary to admit that both above-indicated methods, such as Expansion of elements determinant to any row or column ,as method #1 ,and Laplace’s theorem ,as method #2 ,have the similarity in definition of the value determinant, despite on the difference in formulas for numerical calculations. In practical conditions use of any above-said method for evaluation of the value determinant in general depends from given matrix in numerical data and this factor should to take into consideration in period of hard calculation processes. And with goal of express evaluation of the matrix determinants and reducing of calculation procedures recommend to use the considered functional graphs and formulas for given matrix in numerical data...
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About the Book
This book is designed for wide use in colleges and universities by beginners and more advanced students in studying of Linear Algebra and Programming .Its features and considered methods in general concern to evaluation of matrix determinant by Laplace’s and Expansion methods with use of functional graphs and includes the following aspects: The general principles of Laplace’s and Expansion methods Functional graphs and algorithms for Laplace’s method in process of evaluation of matrix determinant for the different rows and columns(on base of 4∙4 and 5∙5 matrices) Functional graphs and algorithms for Expansion method in process of evaluation of matrix determinant for the different rows and columns (on base of 4∙4 and 5∙5 matrices) Evaluation of some main properties of matrix determinant in examples Practical numerical data for above-considered conditions with solving of multiply linear equations
About the Author
Anatoly Rozenblat came to the United States in 1990 from former Soviet Union with status refugee. As a creative personality, inventor and scientist, he received a fundamental technical and arts education in Marine (Mechanical) and Manufacturing Engineering. Rozenblat holds a bachelor of science degree in Mechanical Engineering from the Odessa Institute of Maritime Transport Engineering and a bachelor of science degree in Computer and Information systems from Chicago East-West University. He participated in the US SBA Program (NASA, Energy, etc.. Many his new innovations were described by NCIO (USA) in the newsletter American Inventor in an article “Inventor from Russia brings the new technologies to US” and Catalogs. His biography has been published by the International Biographical Centre, England; the American Biographical Institute; and Marquis’ Who’s who in America. He was also invited to the twenty-sixth, twenty-seventh and other Israel Conferences on Mechanical Engineering.