Chapter 3 Linear Codes
... of its parity-check matrix must be linearly independent, but that some 3 columns are linearly dependent. Definition 3.18 (Syndrome). Suppose H is a parity-check matrix of an [n, k] linear code C. Then for any vector u ∈ Fqn , the column vector Hut is called the syndrome of u, denoted S(u). Remark. ...
... of its parity-check matrix must be linearly independent, but that some 3 columns are linearly dependent. Definition 3.18 (Syndrome). Suppose H is a parity-check matrix of an [n, k] linear code C. Then for any vector u ∈ Fqn , the column vector Hut is called the syndrome of u, denoted S(u). Remark. ...
Toeplitz Transforms of Fibonacci Sequences
... and a = −1, the proof shows that the element of R(a, b) beginning with s0 = 1 and s1 = 1 has perfect square pn (s) for n ≥ 4. In this case (sn ) is the constant 1 sequence, and the inverse image of τ (s) contains exactly two elements, the additional one being the alternating sequence 1, −1, 1, −1, . ...
... and a = −1, the proof shows that the element of R(a, b) beginning with s0 = 1 and s1 = 1 has perfect square pn (s) for n ≥ 4. In this case (sn ) is the constant 1 sequence, and the inverse image of τ (s) contains exactly two elements, the additional one being the alternating sequence 1, −1, 1, −1, . ...
Module Fundamentals
... Proof. The correspondence theorem for groups yields a one-to-one correspondence between additive subgroups of M containing N and additive subgroups of M/N . We must check that submodules correspond to submodules, and it is sufficient to show that if S1 /N ≤ S2 /N , then S1 ≤ S2 (the converse is immedi ...
... Proof. The correspondence theorem for groups yields a one-to-one correspondence between additive subgroups of M containing N and additive subgroups of M/N . We must check that submodules correspond to submodules, and it is sufficient to show that if S1 /N ≤ S2 /N , then S1 ≤ S2 (the converse is immedi ...
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... significant); however, F also satisfies the constraint det F = 0 which removes one degree of freedom. (v) F is a correlation, a projective map taking a point to a line (see definition 1.28(p39)). In this case a point in the first image x defines a line in the second l0 = Fx, which is the epipolar li ...
... significant); however, F also satisfies the constraint det F = 0 which removes one degree of freedom. (v) F is a correlation, a projective map taking a point to a line (see definition 1.28(p39)). In this case a point in the first image x defines a line in the second l0 = Fx, which is the epipolar li ...
Construction of Transition Matrices for Reversible Markov Chains
... Author’s Declaration of Originality I hereby certify that I am the sole author of this major paper and that no part of this major paper has been published or submitted for publication. I certify that, to the best of my knowledge, my major paper does not infringe upon anyone’s copyright nor violate a ...
... Author’s Declaration of Originality I hereby certify that I am the sole author of this major paper and that no part of this major paper has been published or submitted for publication. I certify that, to the best of my knowledge, my major paper does not infringe upon anyone’s copyright nor violate a ...
Fraction-free matrix factors: new forms for LU and QR factors
... Various applications including robot control and threat analysis have resulted in developing efficient algorithms for the solution of systems of polynomial and differential equations. This involves significant linear algebra subproblems which are not standard numerical linear algebra problems. The “ ...
... Various applications including robot control and threat analysis have resulted in developing efficient algorithms for the solution of systems of polynomial and differential equations. This involves significant linear algebra subproblems which are not standard numerical linear algebra problems. The “ ...
CHARACTERISTIC ROOTS AND VECTORS 1.1. Statement of the
... 1.5. Characteristic vectors. Now return to the general problem. Values of λ which solve the determinantal equation are called the characteristic roots or eigenvalues of the matrix A. Once λ is known, we may be interested in vectors x which satisfy the characteristic equation. In examining the genera ...
... 1.5. Characteristic vectors. Now return to the general problem. Values of λ which solve the determinantal equation are called the characteristic roots or eigenvalues of the matrix A. Once λ is known, we may be interested in vectors x which satisfy the characteristic equation. In examining the genera ...
Convergence of the solution of a nonsymmetric matrix Riccati
... Preprint submitted to Elsevier Science ...
... Preprint submitted to Elsevier Science ...
Linear Maps - UC Davis Mathematics
... 6 THE MATRIX OF A LINEAR MAP ((1, 2), (0, 1)) of R2 we have S(1, 2) = (2, 1) = 2(1, 2) − 3(0, 1) and S(0, 1) = (1, 0) = 1(1, 2) − 2(0, 1), so that ...
... 6 THE MATRIX OF A LINEAR MAP ((1, 2), (0, 1)) of R2 we have S(1, 2) = (2, 1) = 2(1, 2) − 3(0, 1) and S(0, 1) = (1, 0) = 1(1, 2) − 2(0, 1), so that ...
Some algebraic properties of differential operators
... Let K be a differential field with derivation ∂ and let K[∂] be the algebra of differential operators over K. First, we recall the well-known fact that the ring K[∂] is left and right Euclidean, hence it satisfies the left and right Ore conditions. Consequently, we may consider its skewfield of frac ...
... Let K be a differential field with derivation ∂ and let K[∂] be the algebra of differential operators over K. First, we recall the well-known fact that the ring K[∂] is left and right Euclidean, hence it satisfies the left and right Ore conditions. Consequently, we may consider its skewfield of frac ...
Monahan, J.F.Two Algorithms for Analysis of ARMA Time Series Models."
... covariance (precision, in this case) matrix between the maximum likelihood and the Bayesian methods is the computation of a and b, which is not a great ...
... covariance (precision, in this case) matrix between the maximum likelihood and the Bayesian methods is the computation of a and b, which is not a great ...
Title and Abstracts - Chi-Kwong Li
... Title: The genus of the boundary generating curves of numerical ranges Abstract: Helton and Vinnikov proved the validity of the Fiedler-Lax conjecture in 2005. Recently Plaumann and Vinzant gave a rather elementary proof of the Helton-Vinnikov theorem. We are interested in concrete construction of h ...
... Title: The genus of the boundary generating curves of numerical ranges Abstract: Helton and Vinnikov proved the validity of the Fiedler-Lax conjecture in 2005. Recently Plaumann and Vinzant gave a rather elementary proof of the Helton-Vinnikov theorem. We are interested in concrete construction of h ...
