Abstract
A matrix \(M \in {M_{n \times m}}(k)\) is an element of a vector space of finite dimension n2. When K = \({\mathbb{R}}\)or K =\({\mathbb{C}}\), this space has a natural topology, that of K nm. Therefore we may manipulate such notions as open and closed sets, and continuous and differentiable functions.
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Serre, D. (2010). Matrices with Real or Complex Entries. In: Matrices. Graduate Texts in Mathematics, vol 216. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7683-3_5
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DOI: https://doi.org/10.1007/978-1-4419-7683-3_5
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