Topics Related to the Factorization of Matrices |
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Page 1
... M. H. Ingraham . The problems are : 1 ) Given a matrix A , whose elements are polynomials in À over a field F , when does there exist a unimodular matrix T such that TA = \ I \ I – X , X having elements in ? This problem plays an ...
... M. H. Ingraham . The problems are : 1 ) Given a matrix A , whose elements are polynomials in À over a field F , when does there exist a unimodular matrix T such that TA = \ I \ I – X , X having elements in ? This problem plays an ...
Page 16
... M. H. Ingraham has studied this problem and has developed an algorithm for finding solutions of this equation if such exist . First he reduces & A¡À , a matrix over F [ ^ ] , to its Hermite canonical form . He then considers all ...
... M. H. Ingraham has studied this problem and has developed an algorithm for finding solutions of this equation if such exist . First he reduces & A¡À , a matrix over F [ ^ ] , to its Hermite canonical form . He then considers all ...
Page
... M. H. Ingraham . To solve the unilateral matrix equation , & A – 0 , over a field F , using the method of M. H. Ingraham , it is necessary to determine whether or not the matrix M = Σ Σ Â ̧Àa has a right divisor in the form I - 1 . By ...
... M. H. Ingraham . To solve the unilateral matrix equation , & A – 0 , over a field F , using the method of M. H. Ingraham , it is necessary to determine whether or not the matrix M = Σ Σ Â ̧Àa has a right divisor in the form I - 1 . By ...
Common terms and phrases
applied Assume B₂ column common left multiple commutative Consider Corollary defined degree k degree kn degree less direct product elements in F equal equation example exist a unimodular factor family of right follows given greatest common divisor Hence Hermite form involving leading coefficient least common left left associates linear linearly dependent M. H. Ingraham main diagonal element matrices with elements matrix modulo necessary and sufficient non-singular obtained occurs parameter parametric family polynomial principal ideal ring problem proper of degree rank relation relatively prime replaced right divisors rows satisfy shown similar solution solving sufficient condition Suppose Theorem Theorem 1.4 theory thesis triangular true unilateral equation unique solution uniquely determined University of Wisconsin X₂ zero