Construct a lower triangular matrix:

Show the elements:

Normal can convert a LowerTriangularMatrix to its ordinary representation:

Construct a lower triangular matrix with symbolic entries:

Show the elements:

Get the determinant:

LowerTriangularMatrix objects include properties that give information about the matrix:

The "Summary" property gives a brief summary of information about the matrix:

The "StructuredAlgorithms" property lists the functions that have structured algorithms:

Structured algorithms are typically faster:

Compute the determinant:

Compute the inverse:

Solve a linear system:

Compute the eigenvalues:

When appropriate, structured algorithms return another LowerTriangularMatrix object:

Inverting lt gives another lower triangular matrix:

Transposing lt gives an upper triangular matrix:

The product of lt with its transpose is no longer a triangular matrix:

Construct a lower triangular matrix from a SparseArray with integer entries:

Show the elements:

Construct a lower triangular complex-valued matrix:

Compute the determinant:

Compute the inverse:

Solve a linear system:

Compute the eigenvalues:

LUDecomposition by default uses LowerTriangularMatrix for the lower triangular matrix it returns:

Verify the decomposition:

Format the three matrices:

Two n×n matrices:

Form a unit lower triangular matrix of size 3n×3n that has the two matrices as blocks:

The n×n lower-left submatrix of the inverse is equivalent to the product of the two original matrices:

Transposing a LowerTriangularMatrix yields an UpperTriangularMatrix:

The entries of a LowerTriangularMatrix are coerced to the lowest precision:

A full matrix:

LowerTriangularMatrix[a] does not evaluate if a is not manifestly lower triangular:

Use LowerTriangularMatrix[LowerTriangularize[a]] to get the lower triangular part of a:

A Stirling matrix of the first kind:

A Stirling matrix of the second kind:

The two kinds of Stirling matrices are inverses of each other:

A variant of the Pascal matrix with alternating column signs:

Verify that the matrix is involutory (gives the identity matrix when squared):