# 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.