Abstract
In this chapter we provide the necessary background from the theory of complex numbers. Then we describe the basic properties of polynomials and their roots. We introduce the concept of determinants, establish their properties, and present the basic theory of systems of linear algebraic equations with nonsingular matrices. The main types of rectangular matrices are described.
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Notes
- 1.
Abraham de Moivre (1667–1754) was a French mathematician.
- 2.
Here and below, the symbol \(\Box \) indicates the end of a proof.
- 3.
William George Horner (1786–1837) was a British mathematician.
- 4.
Étienne Bézout (1730–1783) was a French mathematician.
- 5.
François Viète (1540–1603) was a French mathematician.
- 6.
Leopold Kronecker (1823–1891) was a German mathematician.
- 7.
Alexandre-Théophile Vandermonde (1735–1796) was a French musician and mathematician.
- 8.
Gabriel Cramer (1704–1752) was a Swiss mathematician.
- 9.
Joseph-Louis Lagrange (1736–1813) was a French mathematician.
- 10.
Johann Carl Friedrich Gauss (1777–1855) was a German mathematician.
- 11.
Charles Hermite (1822–1901) was a French mathematician.
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Beilina, L., Karchevskii, E., Karchevskii, M. (2017). Preliminaries. In: Numerical Linear Algebra: Theory and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-57304-5_1
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DOI: https://doi.org/10.1007/978-3-319-57304-5_1
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