Tag Archives: Cauchy Schwarz inequality

Math2111: Chapter 1: Fourier series. Section 2: Inner product and norm

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

We repeat two fundamental concepts which you should have seen in linear algebra already.
Inner product and norm in \small \mathbb{R}^n
Let \boldsymbol{u}, \boldsymbol{v} \in \mathbb{R}^n be vectors with

\displaystyle \boldsymbol{u} = (u_1, \ldots, u_n)^\top, \quad \boldsymbol{v} = (v_1,\ldots, v_n)^\top

where (u_1,\ldots, u_n)^\top stands for the transpose of the vector (u_1,\ldots, u_n).

Then the dot product of these vectors is defined by Continue reading