Matakuliah
Tahun
: MATRIX ALGEBRA FOR STATISTICS
: 2009
Trace and Norm
Pertemuan 8
Soal:
1. Show that if x and y are mx1 vectors,
tr(xyT) = xTy. Show that if A and B are
mxm matrices and B is nonsingular,
tr(BAB-1)= tr(A)
2. If A is an mxn matrix, show that tr(ATA) = 0
if and only if A = (0).
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Theorm:
If p is a real number with p ≥ 1 and x is an
nx1 vector, then
is a norm on Rn or Cn called the Lp, norm
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3. If A is a vector
Show that u.Av =AT u.v
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