LowerTriangularize

LowerTriangularize[m]

gives a matrix in which all but the lower triangular elements of m are replaced with zeros.

LowerTriangularize[m,k]

replaces with zeros only the elements above the k^(th) subdiagonal of m.

Details

Examples

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Basic Examples  (2)

Get the lower triangular part of a matrix:

Get the strictly lower triangular part of a matrix:

Scope  (12)

Basic Uses  (8)

Get the lower triangular part of nonsquare matrices:

Find the lower triangular part of a machine-precision matrix:

Lower triangular part of a complex matrix:

Lower triangular part of an exact matrix:

Lower triangular part of an arbitrary-precision matrix:

Compute the lower triangular part of a symbolic matrix:

Large matrices are handled efficiently:

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

Special Matrices  (4)

The lower triangular part of a sparse matrix is returned as a sparse matrix:

Format the result:

The lower triangular part of structured matrices:

The lower triangular part of an identity matrix is the matrix itself:

This is true of any diagonal matrix:

Compute the the lower triangular part, including the superdiagonal, for HilbertMatrix:

Properties & Relations  (2)

Matrices returned by LowerTriangularize satisfy LowerTriangularMatrixQ:

LowerTriangularize[m,k] is equivalent to Transpose[UpperTriangularize[Transpose[m], -k]]:

Wolfram Research (2008), LowerTriangularize, Wolfram Language function, https://reference.wolfram.com/language/ref/LowerTriangularize.html.

Text

Wolfram Research (2008), LowerTriangularize, Wolfram Language function, https://reference.wolfram.com/language/ref/LowerTriangularize.html.

BibTeX

@misc{reference.wolfram_2021_lowertriangularize, author="Wolfram Research", title="{LowerTriangularize}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/LowerTriangularize.html}", note=[Accessed: 25-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_lowertriangularize, organization={Wolfram Research}, title={LowerTriangularize}, year={2008}, url={https://reference.wolfram.com/language/ref/LowerTriangularize.html}, note=[Accessed: 25-September-2021 ]}

CMS

Wolfram Language. 2008. "LowerTriangularize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LowerTriangularize.html.

APA

Wolfram Language. (2008). LowerTriangularize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LowerTriangularize.html