Give the condition for A linear operator T: v- v to be orthogonal.
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Step-by-step explanation:
A linear operator T : V → V is orthogonal if
〈T(u), T(v)〉 = 〈u, v〉 for all u, v ∈ V .
Theorem.
For a linear operator T : V → V , the. following are equivalent:
(a) T is orthogonal;
(b) T preserves all lengths and angles;
(c) ||T(v)|| = ||v|| for any v ∈ V .
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