No, that is not right. The dot product is not a tensor, nor is the result of a dot product a (0,2) tensor-it is a (0,0) tensor a.k.a. scalar.Tzar said:A tensor is simply a multilinear map (a map thats linear in each variable) from a vector space and the dual of the vector space to the Reals.
A very simple example is the dot product. It takes in two 2 vectors and gives a Real number.It is linear in both varibales. Thus the dot product is a (0 2) tensor.
You know that we can take several numbers and form a vector. Simmiliarly we can take N vectors of length N and produce an N by N matrix. One way we could do this is like this:dervast said:What a tensor is .? I have found a text in my book that says that the electric and magnetic constants are tensors.. Do u have something in mind?
Thx a lot
yes, I implied this question in my vector calc thread. I didn't even bother to look it up, because I'm afraid I'll draw misconceptions from laymen explainations (as I have done in the past with relativity and quantum mechanics).Swapnil said:Hi, I have been hearing/reading the word "tensor" a lot lately, but I have no idea what it is or what is it used for. I also googled for it but I get bogged down by so much coplicated mathematics that I am unable to make any sense of it. All I know that tensors have something to do with matrices and special relativity, no more no less. Could someone please just give me a gist of what tensors are?
I can't even begin to express the difficulty imagining this.mathwonk said:think of a taylor series expanded at each point of a space.