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What can you say about the dimensions of A and B_if both products AB and BA are defined, although not necessarily of the same size? Analogously, let T1 : R" T2 : Rk → R" be linear transformations. What can you say about n, k, and m if both compositions T2 • T1 and T1 o T2 are well defined? Rk and

What can you say about the dimensions of A and B_if both products AB and BA are defined, although not necessarily of the same size? Analogously, let T1 : R" T2 : Rk → R" be linear transformations. What can you say about n, k, and m if both compositions T2 • T1 and T1 o T2 are well defined? Rk and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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11. What can you say about the dimensions of A and B if both products AB and BA are defined, although not necessarily of the same size? Analogously, let T1 : R" → R* and T2 : R* compositions T2 o T1 and T1 o T2 are well defined? → R" be linear transformations. What can you say about n, k, and m if both
Transcribed Image Text:11. What can you say about the dimensions of A and B if both products AB and BA are defined, although not necessarily of the same size? Analogously, let T1 : R" → R* and T2 : R* compositions T2 o T1 and T1 o T2 are well defined? → R" be linear transformations. What can you say about n, k, and m if both
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