Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Inner Product Spaces, Orthonormal Basis
Which of the following is an inner product on the vector space of all real-valued continuous functions on [0, 1]?
1
〈f, g〉 = |\(\int_0^1\) f(t) g(t) dt|
2
〈f, g〉 = \(\int_0^1\) |f(t) g(t)| dt
3
〈f, g〉 = f(0) g(0) + f(1) g(1)
4
〈f, g〉 = \(\int_0^1\) f(t) g(t) dt