At_mul_B(A, B)

For matrices or vectors $A$ and $B$, calculates $Aᵀ⋅B$


julia> A = [1 2 3; 4 5 6];
julia> B = [7, 8, 9];
julia> At_mul_B(A, B)
2-element Array{Int64,1}:

This example calculates the dot product of the transpose of matrix A and vector B. The result is an array of length 2.

julia> A = [1 2; 3 4; 5 6];
julia> B = [7 8; 9 10];
julia> At_mul_B(A, B)
2×2 Array{Int64,2}:
 46   52
 64   72

In this example, A is a matrix and B is also a matrix. The function At_mul_B calculates the matrix product of the transpose of A and B, resulting in a 2x2 matrix.

Common mistake example:

julia> A = [1 2 3; 4 5 6];
julia> B = [7, 8];
julia> At_mul_B(A, B)
ERROR: DimensionMismatch("matrix A has dimensions (2, 3), vector B has length 2")

In this example, the dimensions of A and B are incompatible for matrix multiplication. Ensure that the number of columns in A matches the length of B to avoid this error.

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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