Linear transformation properties A linear function T:\mathbb{R}^{n}\rightarrow \mathbb{R}^{n} is given by

Lincoln Hernandez

Lincoln Hernandez

Answered question

2022-02-15

Linear transformation properties
A linear function T:RnRn is given by T(x)=Px,where PT=P1.
Prove that for any two vectors x,yRn we have |T(x)|=|x| and T(x).T(y)=x.y. Also prove that T is continuous.

Answer & Explanation

losse9x1

losse9x1

Beginner2022-02-16Added 12 answers

1. |z|=zTzzRn.
2. xy=xTyx,yRn.
Plug these in, expand T in terms of P and do arithmetic.
EDIT Lets

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