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## Homework Statement

A vector space W over the real numbers is the set of all 2 x 2 Hermitian matrices. Show that the map T defined as:

T(x,y,z,t) =

[t+x y+iz]

[y-iz t-x]

from R4 to W is an isomorphism.

## Homework Equations

## The Attempt at a Solution

I know that for the map to be isomorphic it has to have the following properties:

- one to one (injective) and onto (surjective)

- ker(T) = {0} and range(T) = W

- The inverse map T^-1 has to exist

- dimension of both R4 and W has to be the same.

I don't really know how to apply these properties in showing that the map is isomorphic. Any help would be appreciated. Thanks in advanced!