Abstract
In this chapter we define matrices with their most important operations and we study several groups and rings of matrices. The matrix operations defined in this chapter were introduced by Arthur Cayley (1821–1895) in 1858. His article “A memoir on the theory of matrices” was the first to consider matrices as independent algebraic objects. In our book matrices form the central approach to the theory of Linear Algebra.
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Notes
- 1.
The Latin word “matrix” means “womb”. Sylvester considered matrices as objects “out of which we may form various systems of determinants” (cp. Chap. 5). Interestingly, the English writer Charles Lutwidge Dodgson (1832–1898), better known by his pen name Lewis Carroll, objected to Sylvester’s term and wrote in 1867: “I am aware that the word ‘Matrix’ is already in use to express the very meaning for which I use the word ‘Block’; but surely the former word means rather the mould, or form, into which algebraic quantities may be introduced, than an actual assemblage of such quantities”. Dodgson also objected to the notation \(a_{ij}\) for the matrix entries: “...most of the space is occupied by a number of a’s, which are wholly superfluous, while the only important part of the notation is reduced to minute subscripts, alike difficult to the writer and the reader.”
- 2.
Leopold Kronecker (1823–1891).
- 3.
The term “scalar” was introduced in 1845 by Sir William Rowan Hamilton (1805–1865). It originates from the Latin word “scale” which means “ladder”.
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Liesen, J., Mehrmann, V. (2015). Matrices. In: Linear Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-24346-7_4
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DOI: https://doi.org/10.1007/978-3-319-24346-7_4
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