Functional Analysis II Quiz

Inner product of a and y can be represented as ................ function of a and for each fixed y

• linear
• cubic
• exponential
• quadratic

A closed convex subset C of a Hilbert space H contains a unique vector of ......... norm

• maximum
• average
• infinite
• minimum

If a and b are orthogonal vectors, then the inner product of a and b is equal to

• zero

• one

• two

• three

In a Hilbert space, the norm of a vector is always

• positive

• negative

• zero

• undefined

Every non-zero Hilbert space contains a .........................orthonormal set.

• partial orthonormal
• finite orthonormal
• complete orthonormal
• infinite orthonormal

In a Hilbert space, the norm of a vector is always

• positive

• negative

• zero

• undefined

What is the only vector orthogonal to itself?

• Scalar vector

• Zero vector

• Parallel vector

• Unit vector

The number (x, ei) is called the .............................of x.

• logarithmic form

• radical form

• Fourier Coefficient

• fractional form

A Hilbert space is a ....................... Banach Space

• bounded
• discrete
• complete
• infinite

If M is a proper closed linear subspace of a Hilbert space H, then there exist a non-zero vector zo in H such that.................

• M is not a proper closed linear subspace of H
• M contains only non-zero vectors
• the orthogonal projection of z0 onto M is zero
• the orthogonal projection of z0 onto M is non-zero