# A_mul_Bc

A_mul_Bc(A, B)

For matrices or vectors \$A\$ and \$B\$, calculates \$Aâ‹…Bá´´\$

## Examples

``````julia> A = [1 2; 3 4];
julia> B = [2 0; 1 2];
julia> A_mul_Bc(A, B)
2×2 Array{Int64,2}:
4   4
10  12``````
1. Matrix multiplication:

``````julia> A = [1 2; 3 4];
julia> B = [2 0; 1 2];
julia> A_mul_Bc(A, B)
2×2 Array{Int64,2}:
4   4
10  12``````

This example calculates the matrix product of A and B, which is equal to A multiplied by the complex conjugate of B.

2. Vector multiplication:

``````julia> A = [1, 2];
julia> B = [3, 4];
julia> A_mul_Bc(A, B)
1×1 Array{Int64,2}:
11``````

Here, A and B are treated as vectors and their product is calculated.

3. Complex matrix multiplication:
``````julia> A = [1+2im 2+3im; 3+4im 4+5im];
julia> B = [2-1im 0-2im; 1-3im 2-4im];
julia> A_mul_Bc(A, B)
2×2 Array{Complex{Int64},2}:
3-8im   2-9im
3-22im  10-29im``````

This example demonstrates the multiplication of complex matrices A and B.

Common mistake example:

``````julia> A = [1 2; 3 4];
julia> B = [1, 2];
julia> A_mul_Bc(A, B)
ERROR: MethodError: no method matching A_mul_Bc(::Array{Int64,2}, ::Array{Int64,1})``````

In this example, the mistake is passing a matrix and a vector to `A_mul_Bc` function, which does not have a defined method for this combination. Ensure that the inputs to `A_mul_Bc` are both matrices or both vectors to avoid such errors.