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Similar to the introduced matrices, in the following definition, we introduce the notion of a “vector” from a pure notational perspective as a special case of a matrix.

Definition: Column Vectors and Row Vectors

Let $n\ge 1$ be a natural number. A column vector (or just vector) with $n$ field elements is a matrix over a field $F$ with just one column and many rows, i.e. an element of $M_{m\times 1}(F):$

$$v=\pmatrix{\alpha_1\\\vdots\\\alpha_m}$$

Similarly, a row vector is transposed column vector

$$v^T=\pmatrix{\alpha_1,&\ldots&,\alpha_m}$$

A row vector is an element of $M_{1\times m}(F)$.

Notes

| | | | | created: 2018-04-09 23:38:57 | modified: 2020-11-29 14:13:45 | by: bookofproofs | references: [7937]

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Bibliography (further reading)

[7937] Knabner, P; Barth, W.: “Lineare Algebra – Grundlagen und Anwendungen”, Springer Spektrum, 2013