a prove that if q is an orthogonal matrix then qx x for any vector x rn where denotes the standa

Name: a prove that if q is an orthogonal matrix then qx x for any vector x rn where denotes the standard euclidean norm b prove the converse if qx x for all x rn then q is an orthogonal matrix 90225
Uploaded: 2024-11-02T12:01:22-08:00
Duration: 4 min 21 s
Channel: Likhit Ganedi
Description: a prove that if q is an orthogonal matrix then qx x for any vector x rn where denotes the standard euclidean norm b prove the converse if qx x for all x rn then q is an orthogonal matrix 90225

Question

Tim Thornhill · Accepted Answer

(a) To prove that ||Qx|| = ||x|| for any vector x ∊ Rn, where Q is an orthogonal matrix, we can

Question

(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x ∈ Rn, where ||·|| denotes the standard Euclidean norm. (b) Prove the converse: if ||Qx|| = ||x|| for all x ∈ Rn, then Q is an orthogonal matrix.

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