# Ac_ldiv_Bc

Ac_ldiv_Bc(A, B)

For matrices or vectors \$A\$ and \$B\$, calculates \$Aá´´\$ \ \$Bá´´\$

## Examples

1. Calculate the conjugate transpose of matrices or vectors:

``````julia> A = [1 2; 3 4];
julia> B = [5 6; 7 8];
julia> Ac_ldiv_Bc(A, B)
2×2 Array{Complex{Int64},2}:
19+0im  23+0im
43+0im  53+0im``````

This example calculates the conjugate transpose of matrix A and matrix B.

2. Perform complex matrix multiplication:

``````julia> C = [1+2im 3+4im; 5+6im 7+8im];
julia> D = [9+10im 11+12im; 13+14im 15+16im];
julia> Ac_ldiv_Bc(C, D)
2×2 Array{Complex{Int64},2}:
-42+0im  -50+0im
-90+0im  -114+0im``````

It performs complex matrix multiplication by taking the conjugate transpose of matrix C and matrix D.

3. Calculate the inner product of complex vectors:
``````julia> x = [1+2im, 3+4im, 5+6im];
julia> y = [7+8im, 9+10im, 11+12im];
julia> Ac_ldiv_Bc(x, y)
Complex{Int64}:
-150+0im``````

This example calculates the inner product of complex vectors x and y by taking their conjugate transposes.

Common mistake example:

``````julia> A = [1 2; 3 4];
julia> B = [5 6 7; 8 9 10];
julia> Ac_ldiv_Bc(A, B)
ERROR: DimensionMismatch("A has dimensions (2, 2) but B has dimensions (2, 3)")``````

In this example, the matrices A and B have incompatible dimensions for matrix multiplication. It's important to ensure that the number of columns in A matches the number of rows in B to perform matrix multiplication using `Ac_ldiv_Bc`.