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MatrixDecomposition

Symbols

  • CMRDecomposition
  • CRDecomposition
  • CWBDecomposition
  • Submatrix
  • UVTransposeMatrix
  • UVTranspose
LawrenceWinkler`MatrixDecomposition`
CRDecomposition
​
CRDecomposition[mat,opt:
False
]
Perform CR decomposition of matrix
mat
such that {c,r} = CRDecomposition[
mat
]
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
Clear[A1,c,r,p];​​A1={{1,1,4,5},{2,2,8,9},{3,3,6,7},{4,4,3,6}};​​A1//MatrixForm​​{c,r}=
CRDecomposition
[A1];​​MatrixForm[#]&/@{c,r}
Out[1]//MatrixForm=
1
1
4
5
2
2
8
9
3
3
6
7
4
4
3
6
Out[1]=

1
4
5
2
8
9
3
6
7
4
3
6
,
1
1
0
0
0
0
1
0
0
0
0
1

In[2]:=
{c,r,p}=
CRDecomposition
[A1,True]
Out[2]=
{{{1,4,5},{2,8,9},{3,6,7},{4,3,6}},{{1,1,0,0},{0,0,1,0},{0,0,0,1}},{1,3,4}}
In[3]:=
MatrixForm[#]&/@{c,r,p}
Out[3]=

1
4
5
2
8
9
3
6
7
4
3
6
,
1
1
0
0
0
0
1
0
0
0
0
1
,
1
3
4

SeeAlso
RowReduce
 
▪
QRDecomposition
 
▪
LUDecomposition
 
▪
MatrixRank
RelatedLinks
Gilbert Strang, Linear Algebra for Everyone
https://math.mit.edu/~gs/everyone/lucrweb.pdf
https://blogs.mathworks.com/cleve/2020/10/23/gil-strang-and-the-cr-matrix-factorization/
""

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