Problem 1051. Exact binary matrix factorization

Created by Paul Peeling

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given a binary-valued (only ones and zeroes) MxN matrix C, and K (where K&lt;M and K&lt;N) find a binary-valued MxK matrix A and a binary-valued KxN matrix B such that A*B equals C. e.g. for K = 2, and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[C =\n\n       1     1     1     0\n       0     0     0     0\n       0     1     0     1]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>then one possible solution is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[A =\n\n     0     1\n     0     0\n     1     0\n\nB =\n\n       0     1     0     1\n       1     1     1     0]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For this problem, assume that at least one solution exists.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note that you cannot do matrix multiplication with two logical matrices in MATLAB.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

46 Solutions
13 Solvers

Last Solution submitted on Mar 05, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

@bmtran (Bryant Tran) on 24 Nov 2012

you should probably add an assert statement that checks the size of the output matrices

Khaled Hamed on 24 Nov 2012

I second @bmtran. lu wins!

Paul Peeling on 24 Nov 2012

thanks, I added the extra asserts as you suggest. the other solutions submitted so far look interesting, thanks for them!

Solution Comments

Show comments

Problem Recent Solvers13

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1051. Exact binary matrix factorization

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers13

Suggested Problems

More from this Author5

Problem Tags

Community Treasure Hunt

Problem 1051. Exact binary matrix factorization

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers13

Suggested Problems

More from this Author5

Problem Tags

Community Treasure Hunt

Players