Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Algebra Inner Product Spaces, Orthonormal Basis
Let ℝn, n ≥ 2, be equipped with standard inner product. Let (v1, v2, ..., vn) be n column vectors forming an orthonormal basis of ℝn. Let A be the n × n matrix formed by the column vectors v1, ... vn. Then
1
A = A-1
2
A = AT
3
A-1 = AT
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Det(A) = 1
5
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