Let T R n R n be a linear transformation that preserves lengths that is, T(x) x for all x in R n 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 ...

a To show that T preserves orthogonality we need to demonstrate that for any vectors x and y in Rn i ...

Let T : R n R n be a linear transformation that preserves lengths; that is,

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Let T : Rⁿ →Rⁿ be a linear transformation that preserves lengths; that is, ΙΙT(x)ΙΙ = ΙxΙΙ 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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Linear Algebra And Its Applications

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Let T : R n R n be a linear transformation that preserves lengths; that is,

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a To show that T preserves orthogonality we need to demonstrate that for any vectors x and y in Rn i...View the full answer

Linear Algebra And Its Applications

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