Bilinear form in R^3

[amjadsuhail]

Verify that H: R^3--->R^3 is a bilinear form ........................................... H[(a1,a2,a3), (b1,b2,b3)] = a1b1 - 2a1b2+a2b1- a3b3

in my book (a1,a2,a3) and other vector written in column form.

[timo]

What's the definition of a bilinear form? Why don't you just check the conditions by hand?

[fattyjwoods]

I like your poll!

[Country Boy]

I'm a bit confused by the question. You say "H: R^3--->R^3" but the H given, H[(a1,a2,a3), (b1,b2,b3)] = a1b1 - 2a1b2+a2b1- a3b3

is clearly from R^3 X R^3 to R.