Artificial intelligent assistant

Trivial Problem: Sum of 2 bilinear forms is also a bilinear form I've just been introduced to the concept of a bilinear form, and I'm having trouble understanding how addition is defined with 2 bilinear forms, which a question in a textbook asks: Show the sum of 2 bilinear forms is also a bilinear form.

A bilinear form is just a type of function. Therefore, addition of bilinear forms is just regular function addition: pointwise addition.

If $f, g$ are bilinear forms then

$$(f+g)(v, u) = f(v, u) + g(v, u)$$

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