Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Suppose that L1 : V → W and L2 : W → Z are
linear transformations and E, F, and G are ordered
bases for V, W, and Z, respectively. Show that, if A
represents L1 relative to E and F and B represents
L2 relative to F and G, then the matrix C = BA represents
L2 ◦ L1: V → Z relative to E and G. Hint:
Show that BA[v]E = [(L2 ◦ L1)(v)]G for all v ∈ V.
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