### Linear operators mapping finite dimensional vector spaces are bounded,

#### by ayushkhaitan3437

Theorem: Every linear operator , where is finite dimensional, is bounded.

Proof

where .

What we learn from here is

where

.

Similarly,

where

Another proof of the assertion is

which is a constant.

Note: why does this not work in infinite dimensional spaces? Because the max and min of and might not exist.

Advertisements