Final answer:
To compute the L² norm and Hermitian inner product for each pair of complex-valued functions on the interval [0, 1], we need to define the functions and use the appropriate formulas.
Step-by-step explanation:
To compute the L² norm and Hermitian inner product for each pair of complex-valued functions on the interval [0, 1], we need to define the functions and use the appropriate formulas. Here are the computations for each type of function:
a) Trigonometric functions:
The L² norm of a trigonometric function is given by the integral of the absolute value of the function squared. The Hermitian inner product of two trigonometric functions is given by the integral of the product of the two conjugate functions.
b) Exponential functions:
The L² norm of an exponential function is given by the integral of the absolute value of the function squared. The Hermitian inner product of two exponential functions is given by the integral of the product of the two conjugate functions.
c) Polynomial functions:
The L² norm of a polynomial function is given by the integral of the absolute value of the function squared. The Hermitian inner product of two polynomial functions is given by the integral of the product of the two conjugate functions.
d) Logarithmic functions:
Logarithmic functions are not dimensionless and do not satisfy the conditions for computing L² norms and Hermitian inner products.