March 2020
Intermediate to advanced
384 pages
13h 10m
English
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A.1. Linear algebra
Linear algebra is the study of linear transformations. A linear transformation is a transformation (e.g., a function) in which the sum of the transformation of two inputs separately, such as T(a) and T(b), is the same as summing the two inputs and transforming them together, i.e., T(a + b) = T(a) + T(b). A linear transformation also has the property that T(a × b) = a × T(b). Linear transformations are said to preserve the operations of addition and multiplication since you can apply these operations either before or after the linear transformation and the result is the same.
One informal way to think of this is that linear transformations do not have “economies of scale.” For example, think of a linear transformation as converting ...
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