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Let t rn rn be a linear transformation that preserves

Question: Let T : Rn → Rn be a linear transformation that preserves lengths; that is , ||T (x)|| = ||x|| for all x in Rn.

a. Show that T also preserves orthogonality; that is T(x). T(y) = 0 whenever x.y = 0.

b. Show that the standard matrix of T is an orthogonal matrix.

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Mathematics: Let t rn rn be a linear transformation that preserves

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Mathematics: Let t rn rn be a linear transformation that preserves

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