Transcription of Linear algebra linear transformations transformation linear
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Linear algebra linear transformations transformation linear
Math 115A - Week 1 Textbook sections: covered: What is Linear algebra ? Overview of course What is a vector? What is a vector space? Examples of vector spaces Vector subspaces Span, Linear dependence, Linear independence Systems of Linear equations Bases* * * * *Overview of course This course is an introduction toLinear algebra . Linear algebra is thestudy oflinear transformationsand their algebraic properties. Atransformationis any operation that transforms an input to an out-put. A transformation islinearif (a) every amplification of the inputcauses a corresponding amplification of the output ( doubling of theinput causes a doubling of the output), and (b) adding inputs togetherleads to adding of their respective outputs. [We ll be more preciseabout this much later in the course.] A simple example of a Linear transformation is the mapy:= 3x, wherethe inputxis a real number, and the outputyis also a real , for instance, in this example an input of 5 units causes an outputof 15 units.
include charge, density, speed, length, time, energy, temperature, vol-ume, and pressure. In finance, scalars would include money, interest rates, prices, and volume. (You can think up examples of scalars in chemistry, EE, mathematical biology, or many other fields). • The set of all scalars is referred to as the field of scalars; it is ...
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