Concept

Orthogonality

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.

A square wave built entirely out of round ones

Add enough sine waves together and flat tops and vertical cliffs appear from nothing. Almost — there is a 9% overshoot that never goes away, and it is not a bug.

analysis · fourier series

The dot product is a shadow

Multiply the matching coordinates and add them up. That rule explains nothing, and it hides the fact that the answer is a length — how far one arrow reaches along another, times how long that other one is.

algebra · inner product

The directions a map leaves alone

Almost every arrow comes out of a transformation pointing somewhere else. A few come out pointing exactly where they went in, only longer or shorter. Those few decide nearly everything the map does.

algebra · eigenvectors

Named alongside it

The objects these essays reach for when they reach for this one.

Matrix Basis Characteristic polynomial Continuity Convergence Cosine Determinant Diagonalisation Dot product Eigenvalue Eigenvector Gibbs' phenomenon

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