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kathrynag
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Homework Statement
Let H be the subset of [tex]M_{2}(\Re)[/tex] consisting of all matrices of the form
[tex]\left[a[/tex][tex]\right]-b[/tex]
[tex]\left[b[/tex][tex]\right]a[/tex] for a, b elements of the reals.
1. Show that <complex, +> is isomorphic to <H,+>
2. Show that <complex, .> is isomorphic to <H,.>
Homework Equations
The Attempt at a Solution
Ok, so I need to show one to one and onto.
Then I need to show that [tex]\varphi[/tex](x+y)=[tex]\varphi[/tex](x)+[tex]\varphi[/tex](y)
Ok I'm having problems in what to use for [tex]\varphi[/tex] and I'm not entirely sure I remember matrix addition. Also, how do I define the complex - a+ib or just ib?