Skip to main content Accessibility help
×
×
Home

When Does Rank(A+B)=Rank(A)+Rank(B)?

  • G. Marsaglia (a1) and G. P. H. Styan (a1)
Extract

In a recent note in the Bulletin, Murphy [5] gave a short proof that for complex m×n matrices A and B, r(A+B)=r(A)+r(B) if the rows of A are orthogonal to the rows of B and the columns of A are orthogonal to the columns of B. His proof was elegant and simple, an improvement on an earlier proof of the same result by Meyer [4].

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      When Does Rank(A+B)=Rank(A)+Rank(B)?
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      When Does Rank(A+B)=Rank(A)+Rank(B)?
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      When Does Rank(A+B)=Rank(A)+Rank(B)?
      Available formats
      ×
Copyright
References
Hide All
1. Khatri, C. G., A simplified approach to the derivation of the theorems on the rank of a matrix, J. Maharaja Sayajirao Univ. Baroda, 10 (1961), 1-5.
2. George, Marsaglia, Bounds on the rank of the sum of matrices, Trans, of the Fourth Prague Conf. on Information Theory, Statistical Decision Functions, Random Processes (Prague, August 31-Sept. 11, 1965), Czechoslovak Acad. Sci. (1967), 455-462.
3. George, Marsaglia and Styan, George P. H., Inequalities and equalities for ranks of matrices (to appear).
4. Meyer, C. D., On the rank of the sum of two rectangular matrices, Canad. Math. Bull. 12 (1969), p. 508.
5. Ian S., Murphy, The rank of the sum of two rectangular matrices, Canad. Math. Bull. 13 (1970), p. 384.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed