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A Transfer Device for Matrix Theorems

The author presents a method to transfer matrix identities over the real numbers to matrix identities over an arbitrary commutative ring.  Several examples are given, including \(\det(AB)= \det(A) \det(B) \), the Cayley-Hamilton Theorem, and identities involving adjoint matrices.

Old Node ID: 
3375
MSC Codes: 
15A04
Author(s): 
William Wardlaw (U. S. Naval Academy)
Publication Date: 
Friday, February 5, 2010
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
February, 1986
Subject(s): 
Algebra and Number Theory
Linear Algebra
Matrix Algebra
Topic(s): 
Linear Algebra
Determinants
Matrix Algebra
Flag for Digital Object Identifier: 
Digital Object Identifier: 
10.4169/capsules003375
Publish Page: 
Furnished by JSTOR: 
Rating Count: 
19.00
Rating Sum: 
51.00
Rating Average: 
2.68
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Friday, February 5, 2010
Average: 2.7 (19 votes)

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