Linear Algebra & Matrices — Community Channel — RIDA MATH

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University
The matrix of $d/dx$
Write the matrix of differentiation on the space spanned by $\{1, x, x^2, x^3\}$ . Why is it nilpotent? What is its matrix on $\{\sin x, \cos x\}$ , and what are its eigenvalues?
A strong contribution: Both matrices written with a stated coordinate convention; nilpotency and eigenvalues $\pm i$ explained.
- Lab: Matrix Boundary Lab
- Read: From Function Spaces to Matrix Representation
University
Which spaces are closed under differentiation?
Decide whether each span is closed under $d/dx$ : $\{e^x, xe^x\}$ , $\{\sin x, x\}$ , $\{1/x\}$ , $\{\sin x \cos x, \cos 2x\}$ . For the closed ones, give the matrix.
A strong contribution: Each case justified; the closed cases include a matrix with an explicit basis order.
- Lab: Matrix Boundary Lab

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