MATH215 Lecture : Lecture Notes.pdf
2 Oct 2013
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2. 3 the polar form of a complex number . Inverses of 3 3 and larger matrices . 9. 8 linear operators with respect to any basis. The rst draft of these lecture notes was written during the winter 2013 term. A linear transformation is a function that takes as input an element of some vector space, and returns as output an element of some other vector space. So before we can de ne a linear transformation properly we need to de ne a vector space. De ne j to be a number such that j2 = 1. Remark: most authors use i for this imaginary number; we use j to avoid confusion with using i for current. A complex number is a number of the form z = x + yj, where x, y r. we write c for the set of all complex numbers. We call x the real part of z and we call y the imaginary part.
