Matrices and Determinoids 1 by Cuthbert Edmund Cullis
Matrices and Determinoids 1 - Table of Contents
- 1. Rectangular Matrices and Determinoids
- 2. Affects of Elements and Derived Products
- 3. Sequences and Affects of Derived Sequences
- 4. Derived Matrices and Determinoids
- 5. Expansions of a Determinoid
- 6. Chain of Matrix Factors: Product Properties
- 7. Determinoid of a Matrix Factor Chain
- 8. Matrices of Minor Determinants
- 9. Rank of a Matrix and Row Connections
- 10. Matrix Equations of the First Degree
- 11. Systems of Linear Algebraic Equations
What You Will Learn in Matrices and Determinoids 1
Matrices and Determinoids (Volume 1) by Cuthbert Edmund Cullis is an authoritative, monumental historical treatise published by Cambridge University Press that presents a comprehensive, self-contained theory of non-square matrices and their scalar generalizations. This classic volume guides readers through rectangular matrix algebra, affect algebra of derived sequences, laplace-style determinoid expansions, products of matrix chains, minor determinant matrices, row-column rank equivalences, and first-degree matrix equations with extraordinary mathematical precision and structural depth.
Designed for pure mathematicians, matrix theorists, historians of mathematics, and research algebraists, this foundational work bridges classical 19th-century determinant theory with modern abstract linear algebra. Cullis details step-by-step proofs for generalized determinant evaluation on non-square matrices, explicit algebraic systems of linear equations, and rank invariant properties under matrix multiplication. Whether you are investigating the historical development of linear algebra, analyzing generalized matrix inverses, or studying non-square linear transformations, this book offers an indispensable roadmap.
Recognized globally as a classic masterpiece in early matrix theory, it stands as one of the best foundational references on the theory of determinoids and rectangular matrices. By unifying combinatorial array properties with explicit linear algebraic solutions, it serves as an essential tool for mastering classical matrix theory with confidence.
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
(1868–1954) was a distinguished British mathematician and Hardinge Professor of Higher Mathematics at the University of Calcutta. He is celebrated for his pioneering, multi-volume research on determinoids and non-square matrix theory, which significantly expanded the scope of classical matrix analysis in the early 20th century.
Through Matrices and Determinoids, Cullis delivers an exhaustive, rigorous formulation of generalized matrix operations. His meticulous notation, detailed proofs, and systematic exposition make this text a classic reference for advanced matrix algebra and historical linear analysis valued by mathematicians and historians worldwide.
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