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Matrices are tensors | Tensor algebra episode 4

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Video / channel Intermediate

All Angles

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Description

Matrices are tensors is episode 4 of the Tensor algebra series on the All Angles YouTube channel. The URL is one educational video that reframes matrices through the tensor product of a vector and a dual vector.

It recaps linear maps and basis-change sandwich products, then glues a vector to a one-form to build a bilinear object readable as a map from vectors to vectors or as a function of a vector and a dual vector. The narration covers currying, why a matrix is a row of columns, how transpose fits dual vectors, and how mixed variance recovers the change-of-basis sandwich. Coordinate tensor products are shown by nesting tables rather than flattening early.

Viewers should know basic linear algebra and preferably earlier dual-vector episodes. The tone is intermediate math visualization, not a first matrix tutorial.

Access is a free YouTube video with animated diagrams. Related episodes sit on the same channel series.

It helps graphics and math learners see why matrices transform with both a basis matrix and its inverse, instead of memorizing the formula alone.