Lecture - Linear Algebra I MT22, IV
What is the condition for $A$ to be an orthogonal matrix?
\[A^\top = A^{-1}\]
What is $(Ax)^\top (Ay)$ when $A$ is an orthogonal matrix?
\[x^\top y\]
What is special about $Ax$ when $A$ is an orthogonal matrix?
It doesn’t change the length of the vector.
What are the two operations on a vector space?
- Vector addition
- Scalar multiplication
Other than vector addition and scalar multiplication forming a group, what is the extra condition about scalar multiplication?
It is distributive.
What name is given to the scalars in a vector space?
The base field (typically $\mathbb{R}$).