Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Inner Product Spaces, Orthonormal Basis
Which of the following is incorrect statement
1
In an inner product space, the norm of a vector is defined to be 〈u, u〉.
2
If 〈u, v〉 = 0, then ||u + v|| ≥ ||v||.
3
If either u = 0 or v = 0, then 〈u, v〉 = 0.
4
A sufficient condition for orthogonality of the pair {u, v} is ||u + v|| = ||v - u||.