Inner product7

Check if a form is an inner product
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.3 Solution: Because $A=A^*$,...
Solution to Mathematics for Machine Learning Exercise 3.9
Let $n\in\mathbb N$ and let $x_1,\dots,x_n>0$ be $n$ positive real numbers so that $x_1+\dots+x_n...
Solution to Mathematics for Machine Learning Exercise 3.4
Compute the angle between $$\mathbf x=\begin{bmatrix} 1\\ 2\end{bmatrix},\quad \mathbf y=\begin{bmat...
Solution to Mathematics for Machine Learning Exercise 3.3
Compute the distance between $$\mathbf x=\begin{bmatrix}1\\2\\3\end{bmatrix},\quad \mathbf y=\begin{...
Solution to Mathematics for Machine Learning Exercise 3.2
Consider $\mathbb R^2$ with $\langle ,\rangle$ defined for all $\mathbf x$ and $\mathbf y$ in $\math...
Solution to Mathematics for Machine Learning Exercise 3.1
Show that $\langle ,\rangle$ defined for all $\mathbf x=[x_1,x_2]^\top\in\mathbb R^2$ and $\mathbf y...
Solution to Linear Algebra Hoffman & Kunze Chapter 8.1
Exercise 8.1.1 Let $V$ be a vector space and $(\ | \ )$ an inner product on $V$. (a) Show that $(0|\...