What is the specific matrix representation of the derivative operator on the space of polynomials of degree at most 2 in the basis {1, x, x^2}?
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[[0, 1, 0], [0, 0, 2], [0, 0, 0]]
The derivative operator maps x^n to nx^(n-1), effectively shifting the basis vectors to a lower power. This results in a matrix with zeros on and below the diagonal, which is also nilpotent.
Also asked as:
- In the basis {1, x, x^2}, what 3x3 matrix represents the derivative operator acting on polynomials of degree at most 2?