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2023-12-09 18:17:22 -08:00
parent a5362a2eb9
commit 6a5e02a8ac
27 changed files with 36 additions and 33 deletions

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@ -58,7 +58,7 @@ Can you develop geometric intuition for their sum and difference?
\definition{Euclidean Norm}
A \textit{norm} on $\mathbb{R}^n$ is a map from $\mathbb{R}^n$ to $\mathbb{R}^+_0$ \\
Usually, one thinks of a norm as a way of mesuring \say{length} in a vector space. \\
Usually, one thinks of a norm as a way of measuring \say{length} in a vector space. \\
The norm of a vector $v$ is written $||v||$. \\
\vspace{2mm}

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@ -28,7 +28,7 @@ Show that the dot product is
\begin{itemize}
\item Commutative
\item Distributive $a \cdot (b + c) = a \cdot b + a \cdot c$
\item Homogenous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
\item Homogeneous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
\note{$x \in \mathbb{R}$, and $a, b$ are vectors.}
\item Positive definite: $a \cdot a \geq 0$, with equality iff $a = 0$ \\
\note{$a \in \mathbb{R}^n$, and $0$ is the zero vector.}