({{, (RefLink[LowerTriangularize, paclet:ref/LowerTriangularize])[m] 
gives a matrix in which all but the lower triangular elements of m are replaced with zeros. }, {, (RefLink[LowerTriangularize, paclet:ref/LowerTriangularize])[m,k]
replaces with zeros only the elements above the k(^th) subdiagonal of m.}})

OpenersNotesSection(Spacer1)Details

(RefLink[LowerTriangularize, paclet:ref/LowerTriangularize])[m] works even if m is not a square matrix.

In (RefLink[LowerTriangularize, paclet:ref/LowerTriangularize])[m,k], positive k refers to subdiagonals above the main diagonal and negative k refers to subdiagonals below the main diagonal.

(RefLink[LowerTriangularize, paclet:ref/LowerTriangularize]) works with (RefLink[SparseArray, paclet:ref/SparseArray]) objects.

OpenersPrimaryExamplesSection(Spacer1)Examples  (6)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Get the lower triangular part of a matrix:

MatrixForm[LowerTriangularize[{{1,2,3},{4,5,6},{7,8,9}}]]

Get the strictly lower triangular part of a matrix:

MatrixForm[LowerTriangularize[{{1,2,3},{4,5,6},{7,8,9}},-1]]

OpenersExampleSection1(Spacer1)Scope  (2)

Get the lower triangular part of nonsquare matrices:

MatrixForm[LowerTriangularize[{{1,2,3,4},{5,6,7,8},{9,10,11,12}}]]

MatrixForm[LowerTriangularize[{{1,2,3},{4,5,6},{7,8,9},{10,11,12}}]]

The number of rows or columns limits the meaningful values of the parameter k:

Table[MatrixForm[LowerTriangularize[{{1,2,3,4},{5,6,7,8},{9,10,11,12},{13,14,15,16}}, k]],{k,-4,3}]

OpenersExampleSection3(Spacer1)Properties & Relations  (2)

Matrices returned by (RefLink[LowerTriangularize, paclet:ref/LowerTriangularize]) satisfy (RefLink[LowerTriangularMatrixQ, paclet:ref/LowerTriangularMatrixQ]):

LowerTriangularMatrixQ[LowerTriangularize[{{a,b},{c,d}}]]

LowerTriangularMatrixQ[LowerTriangularize[{{a,b},{c,d}},1],1]

(RefLink[LowerTriangularize, paclet:ref/LowerTriangularize])[m,k] is equivalent to (RefLink[Transpose, paclet:ref/Transpose])[(RefLink[UpperTriangularize, paclet:ref/UpperTriangularize])[(RefLink[Transpose, paclet:ref/Transpose])[m], -k]]:

m = RandomReal[1,{3,5}];
k = RandomInteger[{-2,4}];
{MatrixForm[l =LowerTriangularize[m,k]], l === Transpose[UpperTriangularize[Transpose[m], -k]]}

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[UpperTriangularize, paclet:ref/UpperTriangularize])  ▪  (RefLink[LowerTriangularMatrixQ, paclet:ref/LowerTriangularMatrixQ])  ▪  (RefLink[Diagonal, paclet:ref/Diagonal])  ▪  (RefLink[Band, paclet:ref/Band])  ▪  (RefLink[LUDecomposition, paclet:ref/LUDecomposition])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Parts of Matrices, paclet:guide/PartsOfMatrices])}, {▪(RefLinkPlain[Linear Systems, paclet:guide/LinearSystems])}})}})