Linear Algebra

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.

Departments of Medicine (Cardiology) and Integrative Biology and Physiology, University of California Los Angeles, Los Angeles, CA, USA
Alan Garfinkel
Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, CA, USA
Jane Shevtsov
Los Angeles, CA, USA
Yina Guo

Authors

Alan Garfinkel
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Jane Shevtsov
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Yina Guo
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Correspondence to Alan Garfinkel .

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