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Dirk Gregorius

Tensor product

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Given two 3D vectors a and b. If I build the product a * Transpose(b) the result is a 3x3 matrix and this operation is called "tensor product"? Is this correct - I really can't remember :-( -Dirk

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You can called it that, but I prefer "outer product" myself (switch the vectors around and you get the inner product). Basically, if you aren't intending to work with tensors, you probably don't want to call it that.

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Yes...sort of.

Usually the product a * transpose(b), where a and b are n-vectors, is called the outer product (as opposed to the inner or "dot" product) and is indeed a nxn matrix.

But the term tensor product is more general than that - the outer product is an example of a tensor product, so you're correct there, but there are lots of other tensor products as well so the term "tensor product" is not defined by that operation.

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It's a common thing to call this operation a dyadic product.
Although tensor product and outer product are common as well.

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Quote:
Original post by DonDickieD
I heard these names as well. But I always thought that "outer product" was another name for the cross product?


No, the cross product isn't the same as the outer product.

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