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Sorcerer

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So I'm reading through some stuff trying to learn tensors, and I wanted to stop myself to grasp this concept before I go further.

Along the way it was mentioned in one of the sources I'm looking at that other than the dot product and cross product, you could multiply vectors in another way, and example given was

If

But which type of multiplication are we talking about here with

Along the way it was mentioned in one of the sources I'm looking at that other than the dot product and cross product, you could multiply vectors in another way, and example given was

**UV**forming a dyad. This was their definition:**UV**= u

_{1}v

_{1}

**ii**+ u

_{1}v

_{2}

**ij**+ u

_{1}v

_{3}

**ik**+ u

_{2}v

_{1}

**ji**+ ...

**, what does**

So my question isSo my question is

**ii**or**ij**even mean? This is multiplication of unit vectors, obviously, but what kind? Dot product? Cross product? That's what I don't understand here.If

**i**= (1, 0, 0) and**j**= (0, 1, 0), then**i ⋅ j**is obviously zero, and**i**X**j**= (0,0,1) =**k**.But which type of multiplication are we talking about here with

**ii**and**ij**and so on? Is it something else entirely? Or do we just leave it like that, and it just means each component has two directions? (not that I can't fathom of a vector doing that, but of course, a dyad isn't a vector, right?)Any insight is welcome. Thanks.
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