Viewing C
4 and M2,2(C) as vector spaces over C with the usual vector space operations,
the s...
Mathematics, 06.03.2021 04:10, curtisepps
Viewing C
4 and M2,2(C) as vector spaces over C with the usual vector space operations,
the set
B =
1 0
0 1
,
1 0
0 β1
,
0 1
1 0
,
0 βi
i 0
is a basis for M2,2(C) (in fact, B \ {I2} are called the Pauli matrices :D). Suppose T : M2,2(C) β C
4
is
a linear map such that
T
1 0
0 1 = (2, 1, 0, β1) T
1 0
0 β1
= (0, 1, 2, β1)
T
0 1
1 0 = (0, 3, 0, β3) T
0 βi
i 0
= (0, β1, 0, 1).
Determine the value of
T
z w
u v
for all z, w, u, v β C.
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