Abstract
The algebra of matrices is to be developed—from scratch. It is from scratch since the familiar rules of the arithmetic and algebra of numbers, learnt in the schoolroom, cannot be translated as they are to new entities called matrices. Where can we seek guidance in constructing the new algebra? Determinants are no help; they are real numbers and obey the familiar rules. Complex numbers (4.5 above) may be better—with appropriate conventions, they can be manipulated by familiar algebraic processes. The question is: can the same trick be turned for matrix algebra? The answer is broadly: despite attempts to define operations with matrices so that matrix algebra is as similar to elementary algebra as possible, there still remain vital differences.
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References
Aitken (A. C.) (1939, 1949): Determinants and Matrices (Oliver and Boyd, First Ed. 1939, Sixth Ed. 1949), Chapters I and III.
Birkhoff (G.) and MacLane (S.) (1941): A Survey of Modern Algebra (Macmillan, 1941), Chapters VIII and X.
Debreu (G.) and Herstein (I. N.) (1953): “Non-negative Square Matrices”, Econometrica, 21, 597–606.
Ferrar (W. L.) (1941): Algebra (Oxford, 1941), Chapters VI–IX.
Ferrar (W. L.) (1951): Finite Matrices (Oxford, 1951), Chapters I–IX.
Frazer (R. A.), Duncan (W. J.) and Collar (A. R.) (1947): Elementary Matrices (Cambridge, 1947), Chapters I and III.
Kemeny (J. G.), Snell (J. L.) and Thompson (G. L.) (1957): Introduction to Finite Mathematics (Prentice-Hall, 1957), Chapter V.
Littlewood (D. E.) (1950): University Algebra (Heinemann, 1950), Chapters I and II.
Murdoch (D. C.) (1957): Linear Algebra for Undergraduates (Wiley, 1957), Chapters 2 and 3.
Thrall (R. M.) and Tornheim (L.) (1957): Vector Spaces and Matrices (Wiley, 1957), Chapters 2 and 3.
Tintner (G.) (1952): Econometrics (Wiley, 1952), Appendices.
Wade (T. L.) (1951): Algebra of Vectors and Matrices (Addison-Wesley Press, 1951), Chapters 1, 5, 6, and 9.
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© 1959 R. G. D. Allen
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Allen, R.G.D. (1959). Mathematical Analysis: Matrix Algebra. In: Mathematical Economics. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-81547-0_13
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DOI: https://doi.org/10.1007/978-1-349-81547-0_13
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