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