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Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Mathematics and Algorithms
>
Matrices and Linear Algebra
>
Parts of Matrices
>
Built-in
Mathematica
Symbol
LowerTriangularize
Diagonal
Band
LUDecomposition
See Also »
|
Linear Systems
Matrices and Linear Algebra
Parts of Matrices
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Lists and Matrices
New in 7.0: Mathematics & Algorithms
More About »
UpperTriangularize
UpperTriangularize
[
m
]
gives a matrix in which all but the upper triangular elements of
m
are replaced with zeros.
UpperTriangularize
[
m
,
k
]
replaces with zeros only the elements below the
k
subdiagonal of
m
.
MORE INFORMATION
UpperTriangularize
[
m
]
works even if
m
is not a square matrix.
In
UpperTriangularize[
m
,
k
]
positive
k
refers to subdiagonals above the main diagonal and negative
k
refers to subdiagonals below the main diagonal.
UpperTriangularize
works with
SparseArray
objects.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
Get the upper triangular part of a matrix:
Get the strictly upper triangular part of a matrix:
Get the upper triangular part of a matrix:
In[1]:=
Out[1]//MatrixForm=
Get the strictly upper triangular part of a matrix:
In[1]:=
Out[1]//MatrixForm=
Scope
(2)
Get the upper triangular part of nonsquare matrices:
The number of rows or columns limits the meaningful values of the parameter
k
:
Properties & Relations
(1)
UpperTriangularize
[
m
,
k
]
is equivalent to
Transpose
[
LowerTriangularize
[
Transpose
[
m
], -
k
]]
:
SEE ALSO
LowerTriangularize
Diagonal
Band
LUDecomposition
MORE ABOUT
Linear Systems
Matrices and Linear Algebra
Parts of Matrices
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Lists and Matrices
New in 7.0: Mathematics & Algorithms
RELATED LINKS
Demonstrations with UpperTriangularize
(
Wolfram Demonstrations Project
)
New in 7