The length of v = (3, 4) is:
Inner Product, Length and Orthogonality
The dot product, length and unit vectors, distance, orthogonal vectors and the Pythagorean theorem, orthogonal complements, and (Row A)⊥ = Nul A.
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CS 223: Computational Linear Algebra
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Notes
u · v = uᵀv. ‖v‖ = √(v · v). Unit vector: v/‖v‖. dist(u, v) = ‖u − v‖.
Exam angle
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Notes
u ⊥ v ⇔ u · v = 0 ⇔ ‖u + v‖² = ‖u‖² + ‖v‖².
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Notes
W⊥ = vectors orthogonal to every vector in W. (Row A)⊥ = Nul A and (Col A)⊥ = Nul Aᵀ.
Exam angle
Related question: this topic is examined
Related question: this topic is examined
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