# tril(M)

tril(M)

Lower triangle of a matrix.

## Examples

1. Extract the lower triangle of a matrix:

``````julia> A = [1 2 3; 4 5 6; 7 8 9];
julia> tril(A)
3×3 Array{Int64,2}:
1  0  0
4  5  0
7  8  9``````

This example extracts the lower triangle of matrix `A` and replaces the upper triangle with zeros.

2. Specify the superdiagonal offset:
``````julia> B = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16];
julia> tril(B, 1)
4×4 Array{Int64,2}:
1   0   0   0
5   6   0   0
9  10  11   0
13  14  15  16``````

Here, the lower triangle of matrix `B` starting from the first superdiagonal (k=1) is extracted.

Common mistake example:

``````julia> C = [1 2 3; 4 5 6; 7 8 9];
julia> tril(C, -1)
ERROR: ArgumentError: k must be non-negative``````

In this example, a negative value for `k` is provided, which is not allowed. The `k` parameter should be non-negative. Always ensure that `k` is a valid value when using `tril`.

Ac_ldiv_B, Ac_ldiv_Bc, Ac_mul_B, Ac_mul_Bc, Ac_rdiv_B, Ac_rdiv_Bc, At_ldiv_B, At_ldiv_Bt, At_mul_B, At_mul_Bt, At_rdiv_B, At_rdiv_Bt, A_ldiv_Bc, A_ldiv_Bt, A_mul_B!, A_mul_Bc, A_mul_Bt, A_rdiv_Bc, A_rdiv_Bt, Bidiagonal, cond, conv2, det, diag, diagind, diagm, diff, eig, eigvals, eigvecs, expm, eye, full, inv, isdiag, ishermitian, isposdef, isposdef!, issym, istril, istriu, logabsdet, logdet, lyap, norm, qrfact, rank, repmat, rot180, rotl90, rotr90, sortrows, sqrtm, SymTridiagonal, trace, Tridiagonal, tril, tril!, triu, triu!, writedlm,

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