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Diagonal matrices
| Content Provider | Scilit |
|---|---|
| Author | Turnbull, H. W. |
| Copyright Year | 1933 |
| Description | In the following pages I have developed the theory of matrices by resolving them into parallel components arranged diagonally, rather than into the usual rows and columns. This treatment is natural in view of the fundamental fact that the resolution is undestroyed when matrices are formed into products (Theorem 2). It is closely related to the theory of continuants and of continued fractions. Certain features stand out in such a presentation—the distinction between the length and range of a diagonal (§ 4), that between regular and irregular diagonals (§ 6), and the use of equable partition (§ 7). The exact conditions for the existence of an rth root of a given singular matrix are examined in § 9 and summarized under the title, the condition of equability. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/275661D6EBC5CF29494AFC1A6ADAD1DE/S0305004100016406a.pdf/div-class-title-diagonal-matrices-div.pdf |
| Ending Page | 372 |
| Page Count | 26 |
| Starting Page | 347 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100016406 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 29 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1933-07-30 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
