orthogonal AND orthonormal

orthogonal; orthonormal

orthogonal

• dot product = 0
• each vector orthog to all other vectors → mutually orthog → linear indep
• square matrix are orthog if their columns make up orthonormal set of vectors
• for an orthog matrix, its inverse = its transpose ($O^{-1}=O^T$)

orthonormal

• a vector is orthonormal if: orthogonal + of length 1
• orthonormal → also linear indep set → collection of orthonormal vec can be orthonormal basis for a span of S
• transforming into unit vector = multiplying a nonzero vector by the reciprocal of its length to obtain a unit vector = normalizing
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