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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 3

Matrices and determinants

1 Matrices

Matrices originated in the study of linear equations but have now acquired an independent status and constitute one of the most important systems in algebra. They are a rich source of examples of algebraic structures, which we shall study later.

As usual, for any positive integer n, the set {1,…,n} will be denoted by n. The cartesian product m × n is therefore the set

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Definition. Let F be a field and m and n positive integers. A mapping

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is called an m × n matrix over F.

Let A be an m × n matrix ...

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