# SymTridiagonal

```
.. SymTridiagonal(d, du)
Construct a real symmetric tridiagonal matrix from the diagonal and upper diagonal, respectively. The result is of type ``SymTridiagonal`` and provides efficient specialized eigensolvers, but may be converted into a regular matrix with :func:`full`.
```

## Examples

In the Julia programming language, the function `SymTridiagonal(d, du)`

is used to construct a real symmetric tridiagonal matrix from the diagonal and upper diagonal elements. The resulting matrix is of type `SymTridiagonal`

and provides efficient specialized eigensolvers. However, it can also be converted into a regular matrix using the `full`

function.

```
julia> d = [1.0, 2.0, 3.0, 4.0];
julia> du = [2.0, 3.0, 4.0];
julia> matrix = SymTridiagonal(d, du)
4×4 SymTridiagonal{Float64,Array{Float64,1}}:
1.0 2.0 ⋅ ⋅
2.0 2.0 3.0 ⋅
⋅ 3.0 3.0 4.0
⋅ ⋅ 4.0 4.0
```

In this example, a symmetric tridiagonal matrix is created using the diagonal elements `[1.0, 2.0, 3.0, 4.0]`

and the upper diagonal elements `[2.0, 3.0, 4.0]`

. The resulting `SymTridiagonal`

matrix `matrix`

is displayed.

To convert the `SymTridiagonal`

matrix into a regular matrix, you can use the `full`

function:

```
julia> full_matrix = full(matrix)
4×4 Array{Float64,2}:
1.0 2.0 0.0 0.0
2.0 2.0 3.0 0.0
0.0 3.0 3.0 4.0
0.0 0.0 4.0 4.0
```

The `full`

function converts the `SymTridiagonal`

matrix `matrix`

into a regular matrix `full_matrix`

of type `Array{Float64,2}`

.

Note: The `SymTridiagonal`

function is typically used when working with large symmetric tridiagonal matrices where the structure can be exploited for efficient computations.

## See Also

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,## User Contributed Notes

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