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An operation that converts a vector or tensor to a scalar


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Looking for an operation that converts a vector or tensor into a scalar, when the vector or tensor value is large.


For example, if I multiply a row vector by a column vector, I get a scalar but I really need a function that turns a column vector into a scalar, when its value is significantly large, but if the vectors value is small, the function simply returns another vector.


I would like it to work with tensors as well.


I hope you find it an interesting problem - I am looking for a function, which can be an operation, but not another vector.

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Hi there thanks, this will work if the vector or tensor is large but if its small it will not work.

 

But perhaps I could use a limit, so that if the vector or tensor satisfies some value then the norm function is applied, otherwise its left intact, but this seems messy and adhoc.

 

Regards.

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There is no general operation (that I know of) that returns a vector in some circumstances and a scalar in others. I don't see how any operation that would work this way would remain tensor rank correct, and I guess I would question any model that would require this kind of behavior.

 

There may be something out there like that, but I guess I can't envision any practical application of this behavior.

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What do you mean by the value of a vector anyway? I would understand that to be defined in terms of some map from your space of vectors to the field of real numbers (I assume that is the field you are working with). Basically that is a norm.

 

There are other operations that you could use to map a tensor to a scalar. You can use tensor contraction for example; this would give a generalisation of the trace. (I assume you have chosen some metric on R^n or on a manifold and so can raise and lower indices).

 

Like Bignose, I am not aware of any operation like the one you describe.

 

Try to give us an idea of why you need such an operation and that may help us with further ideas.

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