1. Consider the vectors |) = 2|01) + 3i|02) and [x) = 511) + (3 - 4i) |02), where [01) and 2) are orthonormal, i.e. (x\Pm) = 8km, where 8km = 1 for k = m and 8km = 0 for k = m. (c) Calculate the inner products (lx) and (xl). Are they equal? (d) Show that y) and [x) satisfy the Cauchy-Schwarz inequality and the triangle inequality.
1. Consider the vectors |) = 2|01) + 3i|02) and [x) = 511) + (3 - 4i) |02), where [01) and 2) are orthonormal, i.e. (x\Pm) = 8km, where 8km = 1 for k = m and 8km = 0 for k = m. (c) Calculate the inner products (lx) and (xl). Are they equal? (d) Show that y) and [x) satisfy the Cauchy-Schwarz inequality and the triangle inequality.
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Transcribed Image Text:1. Consider the vectors |) = 2|p1) + 3i|p2) and [x) = 5|61) + (3 - 4i) |02), where [01)
and 2) are orthonormal, i.e. (klom) = 8km, where 8km = 1 for k = m and 8km = 0
for k = m.
(c) Calculate the inner products (lx) and (xl). Are they equal?
(d) Show that y) and Ix) satisfy the Cauchy-Schwarz inequality and the triangle
inequality.
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