%0 Journal Article %1 citeulike:10273924 %A Brualdi, Richard A. %A Quinn Massey, Jennifer J. %D 1993 %J College Math Journal %K 15-01-linear-and-multilinear-algebra-matrix-theory-instructional-exposition 05c50-graphs-and-linear-algebra 05-01-combinatorics-instructional-exposition %N 1 %P 10--19 %T Some Applications of Elementary Linear Algebra in Combinatorics %V 24 %X Linear algebra has been used with great effectiveness in combinatorics and graph theory. It is sometimes surprising how elementary ideas of linear algebra have far reaching consequences. What are these elementary ideas? Linear independence, rank, determinant, eigenvalues, dimension. Ideas that one learns about in a first course in linear algebra. In this note we discuss three applications which are accessible to good students in a first course. Of these, two can be obtained by purely combinatorial arguments, but all the known arguments for the third use ideas from linear algebra.

@article{citeulike:10273924, abstract = {{Linear algebra has been used with great effectiveness in combinatorics and graph theory. It is sometimes surprising how elementary ideas of linear algebra have far reaching consequences. What are these elementary ideas? Linear independence, rank, determinant, eigenvalues, dimension. Ideas that one learns about in a first course in linear algebra. In this note we discuss three applications which are accessible to good students in a first course. Of these, two can be obtained by purely combinatorial arguments, but all the known arguments for the third use ideas from linear algebra.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Brualdi, Richard A. and Quinn Massey, Jennifer J.}, biburl = {https://www.bibsonomy.org/bibtex/23ca6559c2e4454dcda95268a39bd1c63/gdmcbain}, citeulike-article-id = {10273924}, citeulike-attachment-1 = {brualdi_93_applications.pdf; /pdf/user/gdmcbain/article/10273924/743606/brualdi_93_applications.pdf; 84fa3e976ed5384b70cb4cef74c9fbb79d152982}, comment = {Appeared as IMA Preprint Series \#918 in Feb. 1992, as communicated to me by merryn, 2012-01-25, and which I attach here.}, file = {brualdi_93_applications.pdf}, interhash = {aef16563fdee5855a90c98fccb22fe2a}, intrahash = {3ca6559c2e4454dcda95268a39bd1c63}, journal = {College Math Journal}, keywords = {15-01-linear-and-multilinear-algebra-matrix-theory-instructional-exposition 05c50-graphs-and-linear-algebra 05-01-combinatorics-instructional-exposition}, number = 1, pages = {10--19}, posted-at = {2012-01-26 22:36:29}, priority = {0}, timestamp = {2023-08-21T02:07:56.000+0200}, title = {{Some Applications of Elementary Linear Algebra in Combinatorics}}, volume = 24, year = 1993 }