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

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 TaxelDec 6 '17 at 3:13

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