Tag Archives: multilinear map

Angle = Volume

This is trippy, and profound. The determinant — which tells you the change in size after a matrix transformation 𝓜 — is just an Instance of the Alternating Multilinear Map. (Alternating meaning it goes + − + − + − + … Continue reading

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Jacobian

In the world of linear approximations of multiple parameters and multiple outputs, the Jacobian is a matrix that tells you: if I twist this knob, how does that part of the output change? Pretend that a through z are parameters, or knobs … Continue reading

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Bilinear maps and dual spaces Think of a function that takes two inputs and gives one output. The + operator is like that. 9+10=19 or, if you prefer to be computer-y about it, plus(9, 10) returns 19. So is the … Continue reading

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