Abstract
In this chapter, we will be studying linear functions in n dimensions. \(f: \mathbb {R}^n \longrightarrow \mathbb {R}^n\).
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- 1.
We will often write the matrix whose components are \(a_{ij}\) as the matrix \([a_{ij}]\).
- 2.
We will later see that these may not be axes in the usual sense, since they could involve complex numbers, but we can still write them down symbolically.
- 3.
Almost all the time. The exceptions are cases in which two equations are multiples of each other, such as \(0=X+Y\) and \(0=2X+2Y\). Try solving these for X and Y; you don’t get a definite answer.
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Garfinkel, A., Shevtsov, J., Guo, Y. (2017). Linear Algebra. In: Modeling Life. Springer, Cham. https://doi.org/10.1007/978-3-319-59731-7_6
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DOI: https://doi.org/10.1007/978-3-319-59731-7_6
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