New Parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and Some Explicit Formulas for Its Logarithm
2021 ◽
Vol 60
◽
pp. 65-81
Keyword(s):
Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $\mathrm{Sp}(2,\bbr)\cong\mathrm{SL}(2,\bbr)$. Relying on the properties of the exponential map $\mathfrak{sl}(2,\bbr)\to\mathrm{SL}(2,\bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups.\\ Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.
2017 ◽
pp. 229-283
2010 ◽
Vol 234
(1)
◽
pp. 305-315
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1982 ◽
Vol 85
(2)
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pp. 566-583
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1997 ◽
Vol 173
(1)
◽
pp. 351-358
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1993 ◽
Vol 27
(1)
◽
pp. 21-27
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2010 ◽
Vol 62
(3)
◽
pp. 563-581
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2020 ◽
pp. 559-610