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3. Let T` : V → W be a linear transformation. V and W be inner product spaces. Show that TT and TT" has exactly the same non-zero eigenvalues. 4. Let L€ L(V.W), where V and Ware inner product spaces. Given orthonormal basis 8 = {u} of V_and_p = {ws of W. suppose we have the following information 2 7 x2 ? 12 6 dim(Range(L)) = 1; 2012 3 12 ? where? are unknown numbers. Determine the Schmidt decomposition of L.

3. Let T` : V → W be a linear transformation. V and W be inner product spaces. Show that TT and TT" has exactly the same non-zero eigenvalues. 4. Let L€ L(V.W), where V and Ware inner product spaces. Given orthonormal basis 8 = {u} of V_and_p = {ws of W. suppose we have the following information 2 7 x2 ? 12 6 dim(Range(L)) = 1; 2012 3 12 ? where? are unknown numbers. Determine the Schmidt decomposition of L.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let T` : V → W be a linear transformation. V and W be inner product spaces. Show that TT and TT" has exactly the same non-zero eigenvalues. 4. Let L€ L(V.W), where V and Ware inner product spaces. Given orthonormal basis 8 = {u} of V_and_p = {ws of W. suppose we have the following information 2 7 x2 ? 12 6 dim(Range(L)) = 1; 2012 3 12 ? where? are unknown numbers. Determine the Schmidt decomposition of L.
Transcribed Image Text:3. Let T` : V → W be a linear transformation. V and W be inner product spaces. Show that TT and TT" has exactly the same non-zero eigenvalues. 4. Let L€ L(V.W), where V and Ware inner product spaces. Given orthonormal basis 8 = {u} of V_and_p = {ws of W. suppose we have the following information 2 7 x2 ? 12 6 dim(Range(L)) = 1; 2012 3 12 ? where? are unknown numbers. Determine the Schmidt decomposition of L.
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