Show that for $n \times n$ orthogonal matrix $A$ that $\operatorname{Cond}(A)\leq n$

How do I start with this question? Do I relate this to rank-nullity theorem?


closed as unclear what you're asking by kimchi lover, Stefan4024, Giuseppe Negro, caverac, Parcly Taxel Dec 6 '17 at 3:13

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  • $\begingroup$ What does "$\text{Cond}(A)$" mean? The condition number of $A$? How's that defined? $\endgroup$ – kimchi lover Dec 2 '17 at 22:33
  • $\begingroup$ Cond(A) is condition number of matrix A (for A is an orthogonal matrix). Cond(A) = |A| . |A^-1| $\endgroup$ – dembrownies Dec 2 '17 at 22:46
  • $\begingroup$ So you start with calculating $\|A\|$ or calculating the singular values of $A$. $\endgroup$ – kimchi lover Dec 2 '17 at 22:47
  • $\begingroup$ It would be easy with calculations (I think) but I need to prove that the statement is true $\endgroup$ – dembrownies Dec 2 '17 at 22:50