Ac_ldiv_Bc(A, B)

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


  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)

    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.

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,

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