A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations

Petrichkovich, V. M.

doi:10.1007/bf02513439

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 1 Suppose the Canonical Diagonal Forra D A Of The Ma...1

Theorem 3 [1] the Factorization A = Bc B ~ Rmm C ~ Rmn Of Th...1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2022

Publication Types

Select...

Article2

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. Let (6) be a factorization of the matrix A corresponding to the factorization (4) of its canonical diagonal form O A, Then, when condition (5) holds, it follows from Theorem 2 of [5] that for the matrices A and B there exist matrices U, Vl, and V2, invertible over R, such that UAVI = D a and UBVz = D 8. Therefore we can write UAVI = UBV2V('ICVI and D A = DB~, where qJ = V~-ICVI.…”

Section: Theorem 1 Suppose the Canonical Diagonal Forra D A Of The Ma...mentioning

confidence: 99%

See 1 more Smart Citation

On the parallel factorization of matrices over principal ideal rings

Petrichkovich¹

1999

J Math Sci

Self Cite

View full text Add to dashboard Cite

Section: Theorem 1 Suppose the Canonical Diagonal Forra D A Of The Ma...mentioning

confidence: 99%

“…Now let A = BC be a factorization of the matrix A parallel to the factorization (4) of its canonical diagonal form D '~. Then [5] there exist matrices U, Vl, and V2, invertible over R, such that…”

Section: Theorem 3 [1] the Factorization A = Bc B ~ Rmm C ~ Rmn Of Th...mentioning

confidence: 99%