Logical matrix: Difference between revisions

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In order to designate the row and column numbers of the matrix, the sets ''X'' and ''Y'' are indexed with positive [[integer]]s: ''i'' ranges from 1 to the [[cardinality]] (size) of ''X'', and ''j'' ranges from 1 to the cardinality of ''Y''. See the article on [[indexed set]]s for more detail.

The [[transpose]] <math>R^T</math> of the logical matrix <math>R</math> of a binary matrixrelation corresponds to the [[converse relation]] R^T.<ref>[[Irving Copi|Irving M. Copilowish]] (December 1948) "Matrix development of the calculus of relations", [[Journal of Symbolic Logic]] 13(4): 193–203 [https://www.jstor.org/stable/2267134?seq=1#page_scan_tab_contents Jstor link]</ref>

===Example===

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* {{Citation |first=J.D. |last=Botha |chapter=31. Matrices over Finite Fields §31.3 Binary Matrices |edition=2nd |editor-last1=Hogben |editor-first1=Leslie|author1-link= Leslie Hogben | title=Handbook of Linear Algebra (Discrete Mathematics and Its Applications) | publisher=Chapman & Hall/CRC |isbn=978-0-429-18553-3 | year=2013 |doi=10.1201/b16113 }}

* {{Citation | last1=Kim | first1=Ki Hang|author-link=Ki-Hang Kim | title=Boolean Matrix Theory and Applications |year=1982| publisher=Dekker| isbn=978-0-8247-1788-9}}

* {{cite journal |author-link=H. J. Ryser |first=H.J. |last=Ryser |title=Combinatorial properties of matrices of zeroes and ones |journal=[[Canadian Journal of Mathematics]] |volume=9 |issue= |pages=371–7 |date=1957 |doi= 10.4153/CJM-1957-044-3|url=}}

* {{cite journal |first=H.J. |last=Ryser |title=Traces of matrices of zeroes and ones |journal=Canadian Journal of Mathematics |volume=12 |issue= |pages=463–476 |date=1960 |doi=10.4153/CJM-1960-040-0 }}

* {{cite journal |first=H.J. |last=Ryser |title=Matrices of Zeros and Ones |journal=[[Bulletin of the American Mathematical Society]] |volume=66 |issue= 6|pages=442–464 |date=1960 |doi= 10.1090/S0002-9904-1960-10494-6|url=https://www.ams.org/journals/bull/1960-66-06/S0002-9904-1960-10494-6/S0002-9904-1960-10494-6.pdf}}

* {{cite journal |author-link=D. R. Fulkerson |first=D.R. |last=Fulkerson |title=Zero-one matrices with zero trace |journal=[[Pacific Journal of Mathematics]] |volume=10 |issue= 3|pages=831–6 |date=1960 |doi= 10.2140/pjm.1960.10.831|url=https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-10/issue-3/Zero-one-matrices-with-zero-trace/pjm/1103038231.pdf}}

* {{cite journal |first1=D.R. |last1=Fulkerson |first2=H.J. |last2=Ryser |title=Widths and heights of (0, 1)-matrices |journal=Canadian Journal of Mathematics |volume=13 |issue= |pages=239–255 |date=1961 |doi=10.4153/CJM-1961-020-3 |url=}}

* {{cite book |author-link=L. R. Ford Jr. |first1=L.R. |last1=Ford Jr. |first2=D.R. |last2=Fulkerson |chapter=II. Feasibility Theorems and Combinatorial Applications §2.12 Matrices composed of 0's and 1's |chapter-url=https://www.degruyter.com/document/doi/10.1515/9781400875184-004/html |title=Flows in Networks |publisher=[[Princeton University Press]] |___location= |date=2016 |orig-year=1962 |isbn=9781400875184 |pages=79–91 |doi=10.1515/9781400875184-004 |mr=0159700}}

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{{DEFAULTSORT:Logical Matrix}}

[[Category:Boolean algebra]]

[[Category:Matrices (mathematics)]]