Inner Product Spaces and Orthogonal Complements
Introduction
The following entries are derived from a relatively large yet concise topic called Inner Product Spaces. I would only focus on two subtopics which are the Inner Product Spaces themselves and Orthogonal Complements. Other essential subtopics would also be posted in the form of background knowledge to ensure the thoroughness of readers' understanding. Please also note that the Cross Products subtopic is not required in the context of MA 26500.
Part 1: Inner Product Spaces
Background Knowledge - The Basics of Vectors
Let
- $ \mathbf{v} = \begin{pmatrix} a \\ b \end{pmatrix} $
which denotes a vector between a point and the origin.
Then the length of v, is given by
- $ \mathbf{\|v\|} = \sqrt{x^2 +y^2} $.
Inner Product Spaces
Part 2: Orthogonal Complements
Background Knowledge - Gram-Schmidt Algorithm
Orthogonal Complements
Part 3: Applications
Generic Homework Problems
Generic Exam Problems
Ryan Jason Tedjasukmana
