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Matrices and Matrix Operations

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Book cover Linear Algebra

Part of the book series: Compact Textbooks in Mathematics ((CTM))

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Abstract

In order to introduce the main ideas of Linear Algebra, we first study matrix algebra. So, the first thing we begin with is the following simple linear equation:

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Notes

  1. 1.

    See Chap. 6 for the definition of matrices through linear transformations.

  2. 2.

    The size of a matrix is described in terms of the rows and columns it contains.

  3. 3.

    This binary operation is defined from \(\mathcal{M}_{m\times n}(\mathbb{K}) \times \mathcal{ M}_{m\times n}(\mathbb{K}) \rightarrow \mathcal{ M}_{m\times n}(\mathbb{K})\) and takes (A, B) from \(\mathcal{M}_{m\times n}(\mathbb{K}) \times \mathcal{ M}_{m\times n}(\mathbb{K})\) to A + B in \(\mathcal{M}_{m\times n}(\mathbb{K})\).

  4. 4.

    Named after the Norwegian mathematician Niels Henrik Abel.

  5. 5.

    As we will see later, the number a + d is called the trace of A, the number ad − bc is called the determinant of A, and the polynomial p(λ) = λ 2 − (a + d)λ + (ad − bc) is called the characteristic polynomial of A. See Definition 7.3.2.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

    Belkacem Said-Houari

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  1. Belkacem Said-Houari
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Said-Houari, B. (2017). Matrices and Matrix Operations. In: Linear Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-63793-8_1

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