Teaching MPPSC Assistant Professor Mock Test Series 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
4
Det(A) = 1