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... and either no solutions or many solutions if that determinant is zero. Since the system of equations Ax =  x has a nontrivial solution x by definition of eigenvalues, and also has the trivial solution, the same is true of the rewritten system ( A  I ) x  0 . It follows that this system has infi ...
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CS 598: Spectral Graph Theory: Lecture 3

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Homework assignment 9 Section 6.2 pp. 189 Exercise 5. Let

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Linear codes, generator matrices, check matrices, cyclic codes

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