- #1
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Homework Statement
Assuming I understand the problem correctly, I need to define the set of all orthogonal matrices.
Homework Equations
The Attempt at a Solution
Per the definition of orthogonal matrix: Matrix ##A\in Mat_n(\mathbb{R})## is orthogonal if ##A^tA = I##
If ##O## is the set of all orthogonal matrices in ##\mathbb{R}## then:
[tex]O = \bigcup_{k=2}^n \{X\in Mat_k(\mathbb{R})\ |\ \ X^tX = I \}[/tex]
I don't see anything wrong with this set, but it seems too naive. Can it be this simple?