Construct a block upper triangular matrix:

Show the elements:

Normal can convert a BlockUpperTriangularMatrix to its ordinary representation:

Construct a block upper triangular matrix with symbolic entries:

Show the elements:

Get the determinant:

BlockUpperTriangularMatrix 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:

Compute the determinant:

Compute the eigenvalues:

When appropriate, structured algorithms return another BlockUpperTriangularMatrix object:

Transposing bu gives a block lower triangular matrix:

The product is no longer a block triangular matrix:

Elements in BlockUpperTriangularMatrix are coerced to the precision of the nonzero elements of the input.

Exact matrix:

Machine-number matrix:

Arbitrary-precision number matrix:

Represent a rectangular block upper triangular matrix:

Show the sizes of the diagonal blocks:

The Kronecker product of an upper triangular matrix and a general square matrix is a block upper triangular matrix:

Upper triangular matrices are treated as block upper triangular matrices with 1×1 diagonal blocks:

If a given matrix cannot be transformed into a block triangular form, BlockUpperTriangularMatrix returns the matrix itself: