The following lecture notes, homeworks and solutions were developed by Dr. N.B. Jacobsen for a course on Linear Systems Theory taught at Columbia University, Dept. of Electrical Engineering, Sping 2012. The primary textbook for the course was "Linear Systems" by Prof. T. Kailath, Stanford University. Secondary reference text: "The Theory of Matrices" Vol. 1 and 2, F.R. Gantmacher.
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Unpublished (handwritten) lecture notes on linear systems:
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Matrix Algebras, Basic Properties of Matrices, Determinants
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notes1.pdf
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Adjoint Matrix, Matrix Inverse, Cramer's Rule, Characteristic Polynomial
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notes2.pdf
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Matrix Minors, Binet-Cauchy Formula, Polynomial Matrices, Invariant Polynomials, Diagonal Form
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notes3.pdf
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Minimal Polynomial, Jordan Form, Cayley-Hamilton Theorem
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notes4.pdf
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Review of Linear Time Invariant Systems, Laplace Transform, Dirac Delta Function
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notes5.pdf
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Homeworks and their solutions (no peaking at the solutions before you try the exercises☺):
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