represents the block lower triangular matrix lmat as a structured array.
Details and Options
- Block lower triangular matrices, when represented as structured arrays, allow for efficient storage and more efficient operations, including Det and LinearSolve.
- A block lower triangular matrix generalizes a lower triangular matrix, where the scalar elements in a lower triangular matrix that are on or below the diagonal are replaced by matrices of appropriate dimensions.
- For a BlockLowerTriangularMatrix sa, the following properties "prop" can be accessed as sa["prop"]:
"Matrix" block lower triangular matrix, represented as a full array "BlockSizes" sizes of the diagonal blocks "RowPermutation" permutation of the rows, represented as a permutation list "ColumnPermutation" permutation of the columns, represented as a permutation list "Properties" list of supported properties "Structure" type of structured array "StructuredData" internal data stored by the structured array "StructuredAlgorithms" list of functions with special methods for the structured array "Summary" summary information, represented as a Dataset
- Normal[BlockLowerTriangularMatrix[…]] gives the block lower triangular matrix as an ordinary list.
Examplesopen allclose all
Basic Examples (2)
Construct a block lower triangular matrix:
Normal can convert a BlockLowerTriangularMatrix to its ordinary representation:
Construct a block lower triangular matrix with symbolic entries:
BlockLowerTriangularMatrix objects include properties that give information about the array:
The "BlockSizes" property gives the dimensions of the diagonal blocks:
The "RowPermutation" property encodes row permutations done to the original matrix:
The "ColumnPermutation" property encodes column permutations done to the original matrix:
The "Summary" property gives a brief summary of information about the array:
The "StructuredAlgorithms" property lists the functions that use the structure of the representation:
Structured algorithms are typically faster:
When appropriate, structured algorithms return another BlockLowerTriangularMatrix object:
Transposing bl gives a block upper triangular matrix:
The product is no longer a block triangular matrix:
Elements in BlockLowerTriangularMatrix are coerced to the precision of the nonzero elements of the input.
Generalizations & Extensions (1)
Properties & Relations (2)
Lower triangular matrices are treated as block lower triangular matrices with 1×1 diagonal blocks:
If a given matrix cannot be transformed into a block triangular form, BlockLowerTriangularMatrix returns the matrix itself:
Wolfram Research (2022), BlockLowerTriangularMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/BlockLowerTriangularMatrix.html.
Wolfram Language. 2022. "BlockLowerTriangularMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BlockLowerTriangularMatrix.html.
Wolfram Language. (2022). BlockLowerTriangularMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BlockLowerTriangularMatrix.html