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Linear Transformations and Matrices

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Abstract

The goal of this chapter is to make a connection between matrices and linear transformations. So, let E and F be two finite-dimensional vector spaces over the same field \(\mathbb{K}\) such that \(\dim _{\mathbb{K}}E = n\) and \(\dim _{\mathbb{K}}F = m\). Then, according to Theorem 4.6.1, both spaces have bases.

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  • DOI: 10.1007/978-3-319-63793-8_6
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Notes

  1. 1.

    See Definition 2.12 for the definition of the minors of a matrix.

  2. 2.

    Idempotent matrices are the matrices associated to projections.

  3. 3.

    In fact if A 2 = kA, then we have tr (A) = k ⋅ rank (A).

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Said-Houari, B. (2017). Linear Transformations and Matrices. In: Linear Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-63793-8_6

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