cmi-entrance 2014 Q17*

cmi-entrance · India · pgmath 10 marks Not Maths

For $F = \mathbb{R}$ and $F = \mathbb{C}$, let $O_n(F) = \left\{A \in M_{n \times n}(F) \mid AA^t = I_n\right\}$.
(A) Show that $O_n(\mathbb{R})$ is compact.
(B) Is $O_n(\mathbb{R})$ connected? Justify.
(C) Is $O_n(\mathbb{C})$ compact? Justify.

For $F = \mathbb{R}$ and $F = \mathbb{C}$, let $O_n(F) = \left\{A \in M_{n \times n}(F) \mid AA^t = I_n\right\}$.\\
(A) Show that $O_n(\mathbb{R})$ is compact.\\
(B) Is $O_n(\mathbb{R})$ connected? Justify.\\
(C) Is $O_n(\mathbb{C})$ compact? Justify.

Paper Questions

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