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Unformatted text preview: and S ≻ 0.
• If A ≻ 0, then X 0 if and only if S 0.
0 if and only if A
0, B T (I − AA† ) = 0 and C − B T A† B
0, where A† is the
T A† B serves as a generalization of the Schur complement in
pseudo-inverse of A. (C − B
the case where A is positive semideﬁnite but singular.)
Prove one of these theorems. (You can choose which one.) 85 11 Circuit design 11.1 Interconnect sizing. In this problem we will size the interconnecting wires of the simple circuit
shown below, with one voltage source driving three diﬀerent capacitive loads Cload1 , Cload2 , and
Cload3 . Cload1 Cload2 Cload3 We divide the wires into 6 segments of ﬁxed length li ; our variables will be the widths wi of the
segments. (The height of the wires is related to the particular IC technology process, and is ﬁxed.)
The total area used by the wires is, of course,
w i li . A=
i We’ll take the lengths to be one, for simplicity. The wire widths must be between a minimum and
maximum allowable value...
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- Fall '13
- The Aeneid