Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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dimension
row
space
of A
row space to column space
Axrow = b
column
space
of A
R"
90°
90°
nullspace
of A
Axnull =0
nullspace to 0
nullspace
of AT
dimension
=n-r
dimension
=m-r
dimension
Figure 4.2: Two pairs of orthogonal subspaces. The dimensions add to n and add to m.
This is the Big Picture-two subspaces in R" and two subspaces in R™.
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Transcribed Image Text:dimension row space of A row space to column space Axrow = b column space of A R" 90° 90° nullspace of A Axnull =0 nullspace to 0 nullspace of AT dimension =n-r dimension =m-r dimension Figure 4.2: Two pairs of orthogonal subspaces. The dimensions add to n and add to m. This is the Big Picture-two subspaces in R" and two subspaces in R™.
Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each
subspace (and put two in the nullspace). Which vectors are orthogonal?
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Transcribed Image Text:Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and put two in the nullspace). Which vectors are orthogonal?
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