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FAQ (Frequently Asked Questions)
Category:
CDS 101/110 Fall 2004
Identifiers: H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L2.1 L2.2 L2.3 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.1 L7.1 L9.1
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How do I determine how many Jordan blocks a matrix will have for a particular eigenvalue?
Submitted by: asa
Submitted on: October 20, 2004
Identifier:
L4.2
The size of a Jordan block m_i is determined from the characteristic polynomial
where n_i is the algebraic multiplicity of the eigenvalue.
The number of Jordan blocks for a particular eigenvalue s = lambda_i is
For more on Jordan Form, see http://mathworld.wolfram.com/JordanCanonicalForm.html.
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Should there be a C in front of the second term of equation 4.10 in textbook?
Submitted by: jianghao
Submitted on: October 22, 2004
Identifier:
L4.2
yes
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On page 100 of textbook, how do we get equation 4.13, and should the line immediately above this equation read "input is a unit step?"
Submitted by: jianghao
Submitted on: October 22, 2004
Identifier:
L4.2
Yes, the above line is "input is a unit step". You just set u=1 in equation (4.10) and use variable replacement of t' = t-tau to get it
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How do we define the derivative of a step function as used in the next line? (If it were differentiable at t=0, it would also be continuous!?). how do we interpret the delta "function" in equation 4.14?
Submitted by: jianghao
Submitted on: October 22, 2004
Identifier:
L4.2
Because the last term in (4.13) is D*u(t), where u(t) is a step function, the derivative of step function is a delta function (with infinite slope at t=0 and total area/intensity being unity). This differentiation is not
explained by a normal concept, instead distribution theory will account for it. Also delta function can exist not only inside an integral, but also outside.
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