# Ac_mul_B

Ac_mul_B(A, B)

For matrices or vectors $A$ and $B$, calculates $Aá´´â‹…B$

## Examples

```
julia> A = [1 2; 3 4];
julia> B = [5, 6];
julia> Ac_mul_B(A, B)
2-element Array{Int64,1}:
17
39
```

This example demonstrates the usage of `Ac_mul_B`

function to calculate the product of the conjugate transpose of matrix `A`

and vector `B`

. The result is a vector obtained by multiplying `Aᴴ`

(conjugate transpose of `A`

) with `B`

.

```
julia> A = [1+2im 3-1im; 5+4im 2+1im];
julia> B = [2+3im, 4-1im];
julia> Ac_mul_B(A, B)
2-element Array{Complex{Int64},1}:
-9 + 27im
34 + 15im
```

In this example, `A`

is a complex matrix and `B`

is a complex vector. The function correctly handles complex values and returns a complex vector as the result.

Common mistake example:

```
julia> A = [1 2; 3 4];
julia> B = [5 6; 7 8];
julia> Ac_mul_B(A, B)
ERROR: DimensionMismatch("A has dimensions (2, 2) but B has dimensions (2, 2)")
```

In this example, the dimensions of `A`

and `B`

are incompatible for matrix multiplication. Make sure the dimensions of the input matrices and vectors are compatible for the operation.

## 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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