# isposdef

isposdef(A) -> Bool

Test whether a matrix is positive definite.

## Examples

1. Check if a matrix is positive definite:

``````julia> A = [4 1; 1 4];
julia> isposdef(A)
true``````

This example checks if the matrix `A` is positive definite and returns `true`.

2. Handle non-positive definite matrix:

``````julia> B = [2 1; 1 2];
julia> isposdef(B)
false``````

It returns `false` since the matrix `B` is not positive definite.

3. Verify positive definiteness of a larger matrix:
``````julia> C = [5 2 1; 2 9 3; 1 3 6];
julia> isposdef(C)
true``````

It checks the positive definiteness of the matrix `C` and returns `true`.

Common mistake example:

``````julia> D = [1 2; 2 1; 1 2];
julia> isposdef(D)
ERROR: MethodError: no method matching isposdef(::Array{Int64,2})``````

In this example, the input matrix `D` is not square, which is a requirement for positive definiteness. Ensure that the matrix passed to `isposdef` is a square matrix to avoid such errors.

## 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

### Add a Note

The format of note supported is markdown, use triple backtick to start and end a code block.

*Required Field
Details

Checking you are not a robot: