tril

Return lower triangular part of symbolic matrix

Description

tril(A) returns a triangular matrix that retains the lower part of the matrix A. The upper triangle of the resulting matrix is padded with zeros.

tril(A,k) returns a matrix that retains the elements of A on and below the k-th diagonal. The elements above the k-th diagonal equal to zero. The values k = 0, k > 0, and k < 0 correspond to the main, superdiagonals, and subdiagonals, respectively.

Examples

Lower Triangular Part of Symbolic Matrix

Display the matrix retaining only the lower triangle of the original symbolic matrix:

syms a b c
A = [a b c; 1 2 3; a + 1 b + 2 c + 3];
tril(A)
ans =
[     a,     0,     0]
[     1,     2,     0]
[ a + 1, b + 2, c + 3]

Triangular Matrix On and Below Specified Superdiagonal

Display the matrix that retains the elements of the original symbolic matrix on and below the first superdiagonal:

syms a b c
A = [a b c; 1 2 3; a + 1 b + 2 c + 3];
tril(A, 1)
ans =
[     a,     b,     0]
[     1,     2,     3]
[ a + 1, b + 2, c + 3]

Triangular Matrix On and Below Specified Subdiagonal

Display the matrix that retains the elements of the original symbolic matrix on and below the first subdiagonal:

syms a b c
A = [a b c; 1 2 3; a + 1 b + 2 c + 3];
tril(A, -1)
ans =
[     0,     0, 0]
[     1,     0, 0]
[ a + 1, b + 2, 0]

Input Arguments

collapse all

Input, specified as a numeric or symbolic matrix.

Diagonal, specified as a numeric or symbolic number.