Mathematics · Linear Algebra
If A is a square matrix of order n and x, y ∈ &DoubleDoubleBracketsCapitalR;n, then the function ⟨x, y⟩A = ⟨Ax, Ay⟩ (where ⟨·,·⟩ is the standard inner product) is an inner product over &DoubleDoubleBracketsCapitalR;n(&DoubleDoubleBracketsCapitalR;) if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Rank(A) < n
- 2Rank(A) = n✓
- 3Kernel(A) ≠ {0}
- 4Rank(A) > n
Correct answer
Rank(A) = n
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