‘Lie algebra’ means Lie algebra over R, and ‘representation’ means finite-dimensional representation over C.
1. Define the exponential eX of a square matrix X, and show that eX is
invertible.
Determine eX in each of the following cases:
X=
X=
0
0
1
0
1
, X=
0
1
, X=
1
0
1
1
1
1
, X=
0
1
, X=
2
0 −1
,
1 0
−1 0
.
0 −1
Which of these 6 matrices X are themselves expressible in the form
X = eY , (a) with a real matrix Y , (b) with a complex matrix Y ?
(Justify your answers in all cases.)
2. Define…
Words 373 - Pages 2