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    Zero State, Stable Equilibrium, Dynamic System

    Could someone please help? The question reads: For which real numbers "k" is the zero state a stable equilibrium of the dynamic system (vector(x))(t+1)=A(vector(x))(t)? A= [0.1 k ## 0.3 0.3] --> a 2 x 2 matrix with ## separating the two rows. So, my thought is I need to find the...
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    Isomorphism and Cyclic Groups

    Homework Statement I need to prove that any isomorphism between two cyclic groups maps every generator to a generator. 2. The attempt at a solution Here what I have so far: Let G be a cyclic group with x as a generator and let G' be isomorphic to G. There is some isomorphism phi: G...
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    Non-Abelian Subgroup Produced by

    This is not a homework question (although the answer will help answer a homework question). I know that a non-Abelian group can have both Abelian and non-Abelian subgroups but can a non-Abelian subgroup be produced by an Abelian group (or must the group be non-Abelian). Any thoughts...
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    Simple Yes or No Will Do Eigenvectors

    Simple Yes or No Will Do.... Eigenvectors Homework Statement I think my prof made a mistake when writing this problem: Find a basis of the space V of all 3 x 3 matrices A for which the vectors <1, 1> and <1, 2> are eigenvectors and thus determine the dimensions of V. Is this problem...
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    Matrix - Inner Products and Dot Products

    Homework Statement Consider a matrix A in R^(nxn) . In R^n for vectors x and y, define the product <x, y> = ((Ax)^t)(Ay). a) For which choices of A is this an inner product? b) For which choices of A is <x, y> = x (dot) y (the dot product)? Homework Equations For inner...
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    Cyclic Subgroups

    Homework Statement Consider the set P15 of all integer numbers less than 15 that are mutually prime with 15: P15 = {1, 2, 4, 7, 8, 11, 13, 14}. It is a group under multiplication modulo 15. (a) P15 has six cyclic groups. Find them. my answer: <3>=<6>=<9>=<12>= {0, 3, 6 , 9, 12}...