Lectures on Modules over Principal Ideal Domains
... extended to a basis of Z as a module over itself. In fact if n 6= 0 ∈ Z, then the set {2, n} is linearly dependent (prove it). In fact, show that any two elements of Z are linearly dependent. 3. For a subset S of a vector space, the following statements are equivalent: (i) S is maximal linearly inde ...
... extended to a basis of Z as a module over itself. In fact if n 6= 0 ∈ Z, then the set {2, n} is linearly dependent (prove it). In fact, show that any two elements of Z are linearly dependent. 3. For a subset S of a vector space, the following statements are equivalent: (i) S is maximal linearly inde ...
Las Vegas algorithms for matrix groups
... number fields are not a priori represented by strings of fixed (polynomially bounded) length; the fact that they actually are is a recent result [BBR]. In our algorithms, we shall assume the knowledge of a superset of the prime divisors of G. This is trivial (above) in the characteristic zero case. ...
... number fields are not a priori represented by strings of fixed (polynomially bounded) length; the fact that they actually are is a recent result [BBR]. In our algorithms, we shall assume the knowledge of a superset of the prime divisors of G. This is trivial (above) in the characteristic zero case. ...
Minimum Polynomials of Linear Transformations
... n-dimensional vector space has degree at most n. We shall show that there is a vector v ∈ V such that mT,v (x) = mT (x). Then, because mT (x) is the T -annihilator of some vector v, and every T annihilator polynomial has degree at most n, then the minimum polynomial of T must also have degree at mos ...
... n-dimensional vector space has degree at most n. We shall show that there is a vector v ∈ V such that mT,v (x) = mT (x). Then, because mT (x) is the T -annihilator of some vector v, and every T annihilator polynomial has degree at most n, then the minimum polynomial of T must also have degree at mos ...
- Free Documents
... cond A maxi i A mini i A A where the i A are the eigenvalues of A. cond A cond A . For unitary or orthogonal matrix A.Conditioning Direct methods Iterative methods Property For every matrix A and every matrix norm. cond A cond A. . The condition number cond A is invariant trough unitary transformati ...
... cond A maxi i A mini i A A where the i A are the eigenvalues of A. cond A cond A . For unitary or orthogonal matrix A.Conditioning Direct methods Iterative methods Property For every matrix A and every matrix norm. cond A cond A. . The condition number cond A is invariant trough unitary transformati ...
Faculty of Engineering - Multimedia University
... message transmission in a digital communication system. The transmitting side of the error-control coding adds redundant bits or symbols to the original information signal sequence. The receiving side of the error-control coding uses these redundant bits or symbols to detect and/or correct the error ...
... message transmission in a digital communication system. The transmitting side of the error-control coding adds redundant bits or symbols to the original information signal sequence. The receiving side of the error-control coding uses these redundant bits or symbols to detect and/or correct the error ...
Instance-optimality in Probability with an ` -Minimization Decoder 1
... for the large range of k. Thus, from this new viewpoint, instance-optimality in probability N performs the same for `N 2 as it does for `1 . There was, however, one dampening factor in the results of [7]. Namely, the decoders used in establishing instance-optimality in probability in `N 2 were compl ...
... for the large range of k. Thus, from this new viewpoint, instance-optimality in probability N performs the same for `N 2 as it does for `1 . There was, however, one dampening factor in the results of [7]. Namely, the decoders used in establishing instance-optimality in probability in `N 2 were compl ...
