Math Is Fun Forum

A.R.

Guest

Projection is a Linear Transformation

I need to show that the projection T: R2 -> R2 onto a vector v = [a,  b] is a linear transformation.

Could anyone point me in the right direction?

Thanks

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Projection is a Linear Transformation

Start by using the definition of a linear transformation.  You want to show that T(a + b) = T(a) + T(b) and T(ka) = kT(a).

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

A.R.

Guest

Re: Projection is a Linear Transformation

So would I try to show the defn of a L.T. using the projection of, say, x onto v.  That is,