Matrices and Determinoids 1 by Cuthbert Edmund Cullis
Matrices and Determinoids 1 - Table of Contents
1. Introduction of Rectangular Matrices and Determinoids
2. Affects of the Elements and Derived Products of a Matrix or Determinoid
3. Sequences and the Affects of Derived Sequences
4. Affects of Derived Matrices and Derived Determinoids
5. Expansions of a Determinoid
6. Properties of a Product Formed by a Chain of Matrix Factors
7. Determinoid of a Product Formed by a Chain of Matrix Factors
8. Matrices of Minor Determinants
9. Rank of a Matrix and Connections Between the Rows of a Matrix
10. Matrix Equations of the First Degree
11. Solution of Systems of Linear Algebraic Equations
What You Will Learn in Matrices and Determinoids 1
"Matrices and Determinoids, Volume I" by "Cuthbert Edmund Cullis" is a classic work in early "linear algebra" that develops matrix theory in a rigorous and systematic way. This book is "Volume 1 of a three-volume series", and it lays the theoretical foundation for the entire set. Cullis is especially known for introducing "determinoids", a generalization of determinants designed to handle rectangular matrices, which was an important step in the historical development of matrix theory.
The volume begins with an introduction to "rectangular matrices" and determinoids, followed by a detailed study of how matrix elements behave and how "derived products" and sequences are formed. Several chapters are devoted to derived matrices and determinoids, including their expansions and algebraic properties. Cullis also carefully analyzes products formed by chains of matrix factors and explains how determinoids behave under such products, using formal proofs and symbolic reasoning.
In the later chapters, the book explores "minor determinants", the "rank of a matrix", and the relationships between rows of a matrix. It concludes with the theory of "matrix equations" and the "solution of systems of linear algebraic equations". Written in a classical and proof-based style, Volume 1 is best suited for advanced students, researchers, and readers interested in the theoretical and historical foundations of "matrix theory" and "determinant generalization".
Book Details & Specifications
Title:
Matrices and Determinoids 1 by Cuthbert Edmund Cullis
Publisher:
Cambridge, University Press
Year:
1913
Pages:
452
Type:
PDF
Language:
English
ISBN-10 #:
1429703601
ISBN-13 #:
978-1429703604
License:
Public Domain Work
Amazon:
Amazon
About the Author: Cuthbert Edmund Cullis
The author
Cuthbert Edmund Cullis
(1875–1954) was a British mathematician known for his contributions to "matrix theory" and "determinant generalization". Educated at Cambridge, he later worked as a professor at the University of Calcutta, where he developed his most important mathematical ideas during the early growth of modern algebra. Cullis is best remembered for introducing "determinoids" and for his three-volume work "Matrices and Determinoids". His research helped expand classical "linear algebra" to include rectangular matrices, and his rigorous, proof-based style remains important in the historical study of "algebraic structures".
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