# Tag Archives: tensor

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Once you’re comfortable with 2-arrays and 2-matrices, you can move up a dimension or two, to 4-arrays or 4-tensors. You can move up to a 3-array / 3-tensor just by imagining a matrix which “extends back into the blackboard”. Like … Continue reading

## 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

## 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

## How to multiply matrices

This is for my homies in math class. Mathematical matrices are blocks of numbers, arrayed in 2-D. (Higher-dimensional arrays are called tensors.) Left “times” right equals target. Each entry in the target is the result of a series of +’s … Continue reading