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Outer Product

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A nxn matrix A whose columns form an orthonormal basis of Rn

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size: mxn

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upper triangular

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size: nxm

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when you have more basis vectors  V₁.....Vn needing orthogonalization

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Matrix R

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Matrix Q

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Rank-Nullity Theorom

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Orthogonal Complement

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unit vectors (length = 1)

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linearly independent

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Orthonormal Vectors

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Orthogonal Vectors

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dot product of vectors = 0