Fal!2001 16.3121-5 SVD Example ●( Consider( wide case 100 500 101「500 010 00.50 0100.50 001 U∑L rh so that 01=5 and 0?=0.5 ≡max.‖Gal=5 mIn Gnl2=0≠ Jwc 2=1 But now consider(tall case) 50 100 10 00.5 01000.5 01 00 001」L00」 U∑VH o that 01=5 and 02=0.5 still G三max lwcl2= IGoWcl2=5=01 min.|Gl2=0.5=02Fall 2001 16.31 21—5 SVD Example • Consider (wide case)    G  w = ∙ 500 0 0.5 0 ¸ = ∙ 1 0 0 1 ¸ ∙ 500 0 0.5 0 ¸ 100 010 001 = UΣV H so that σ1 = 5 and σ2 = 0.5 σ ≡ max kGwwck2 =5= σ1 kwck2=1 σ ≡ min kGwwck2 = 0 6= σ2 kwck2=1 • But now consider (tall case) G˜w =   5 0 0 0.5 0 0   =   100 010 001     5 0 0 0.5 0 0   ∙ 1 0 0 1 ¸ = UΣV H so that σ1 = 5 and σ2 = 0.5 still. σ ≡ max kGwwck2 =5= σ1 kwck2=1 σ ≡ min kwck2=1 kGwwck2 = 0.5 = σ2