$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

# 3.1: Terminology and Notation

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Vectors. We’ll denote vectors in the plane by $$(x, y)$$

## Note

In physics and in 18.02 we usually write vectors in the plane as $$x$$i + $$y$$j. This use of i and j would be confusing in 18.04, so we will write this vector as $$(x, y)$$.

In 18.02 you might have used angled brackets $$\langle x, y \rangle$$ for vectors and round brackets $$(x, y)$$ for points. In 18.04 we will adopt the more standard mathematical convention and use round brackets for both vectors and points. It shouldn’t lead to any confusion.

Orthogonal. Orthogonal is a synonym for perpendicular. Two vectors are orthogonal if their dot product is zero, i.e. v = $$(v_1, v_2)$$ and w = $$(w_1, w_2)$$ are orthogonal if

v $$\cdot$$ w = $$(v_1, v_2) \cdot (w_1, w_2) = v_1w_1 + v_2w_2 = 0.$$

Composition. Composition of functions will be denoted $$f(g(z))$$ or $$f \circ g(z)$$, which is read as '$$f$$ composed with $$g$$'