?? svd.mht
字號:
align=3DABSCENTER> then the SVD for A has the form =20
<CENTER><IMG height=3D76 alt=3D[Graphics:svdgr122.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr122.gif" =
width=3D294=20
align=3DABSCENTER>. </CENTER>
<P>Give the form for the SVD of a 4x5 matrix <IMG height=3D18 =
alt=3D[Graphics:svdgr123.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr123.gif" =
width=3D66=20
align=3DABSCENTER> . =20
<P>(Hint: The matrix has five singular values, but <IMG =
height=3D17=20
alt=3D[Graphics:svdgr124.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr124.gif" =
width=3D36=20
align=3DABSCENTER> does not appear in the decomposition.) =
<BR> =20
<BR>
<HR width=3D"100%">
<P>2. Let <IMG height=3D28 alt=3D[Graphics:svdgr125.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr125.gif" =
width=3D69=20
align=3DABSCENTER>. Following the steps of Proof 1 above, =
define <IMG=20
height=3D32 alt=3D[Graphics:svdgr126.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr126.gif" =
width=3D67=20
align=3DABSCENTER> and <IMG height=3D32 =
alt=3D[Graphics:svdgr127.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr127.gif" =
width=3D78=20
align=3DABSCENTER>. =20
<P>a. Expand <IMG height=3D17 alt=3D[Graphics:svdgr128.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr128.gif" =
width=3D70=20
align=3DABSCENTER> =20
<P>b. After applying trig identities it turns out that <IMG =
height=3D17=20
alt=3D[Graphics:svdgr129.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr129.gif" =
width=3D186=20
align=3DABSCENTER>. =20
<P>Use this fact to find a t so that <IMG height=3D17=20
alt=3D[Graphics:svdgr130.gif]=20
src=3D"http://www.uwlax.edu/faculty/will/svd/svd/svdgr130.gif" =
width=3D91=20
align=3DABSCENTER> =20
<P>c. Using part (b) as a start, give an SVD for <I>A</I>. =20
<BR> </P></TD></TR></TBODY></TABLE>
<HR noShade SIZE=3D1>
=A9 1999 Todd Will <BR><FONT face=3Darial,helvetica><FONT size=3D-1>Last =
Modified:=20
22-Feb-1999</FONT></FONT> <BR> <!--webbot bot=3D"HitCounter" =
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