Transcription of Linear algebra linear transformations transformation linear
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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.
• Linear algebra is the study of the algebraic properties of linear trans-formations (and matrices). Algebra is concerned with how to manip-ulate symbolic combinations of objects, and how to equate one such combination with another; e.g. how to simplify an expression such as (x − 3)(x + 5). In linear algebra we shall manipulate not just ...
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