Typos
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@ -58,7 +58,7 @@ Can you develop geometric intuition for their sum and difference?
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\definition{Euclidean Norm}
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A \textit{norm} on $\mathbb{R}^n$ is a map from $\mathbb{R}^n$ to $\mathbb{R}^+_0$ \\
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Usually, one thinks of a norm as a way of mesuring \say{length} in a vector space. \\
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Usually, one thinks of a norm as a way of measuring \say{length} in a vector space. \\
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The norm of a vector $v$ is written $||v||$. \\
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\vspace{2mm}
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@ -28,7 +28,7 @@ Show that the dot product is
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\begin{itemize}
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\item Commutative
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\item Distributive $a \cdot (b + c) = a \cdot b + a \cdot c$
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\item Homogenous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
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\item Homogeneous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
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\note{$x \in \mathbb{R}$, and $a, b$ are vectors.}
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\item Positive definite: $a \cdot a \geq 0$, with equality iff $a = 0$ \\
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\note{$a \in \mathbb{R}^n$, and $0$ is the zero vector.}
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