Mdthbs

I am trying to create something similar to the below image. I have something but my formatting is a little off. How can I correct the formatting and also add the W1, W2, Wn and D letters on top (not a major issue however)?

documentclass{article}

usepackage{amsmath}

begin{document}



begin{align}

   begin{bmatrix}

           W_{11} \

           W_{12} \

           vdots \

           W_{1n}

   end{bmatrix}

   &+ begin{bmatrix}

           W_{21} \

           W_{22} \

           vdots \

           W_{2n}

       end{bmatrix}

   &+ hdots 

   &+ begin{bmatrix}

           W_{n1} \

           W_{n2} \

           vdots \

           W_{nn}

       end{bmatrix}

   &= begin{bmatrix}

           frac{W_{11} + W_{21} + hdots + W_{n1}}{n} \

           frac{W_{12} + W_{22} + hdots + W_{n2}}{n} \

           vdots \

           frac{W_{1n} + W_{2n} + hdots + W_{nn}}{n}

    end{bmatrix}

end{align}



end{document}

The following sets the arrangement inside an array, with the first row handling the labels on top of each bmatrix, while the second row sets each of the matrices/vectors. arraystretch has been increased to spread the content vertically.

documentclass{article}



usepackage{amsmath}



begin{document}



[

  setlength{arraycolsep}{0pt}% No column separation in array; manual spacing

                               % by supplying empty groups {} around operators

  renewcommand{arraystretch}{1.5}% Stretch out content vertically

  begin{array}{ *{8}{c} }

    % Header row in scriptstyle

    scriptstyle W_1 & & % + 

    scriptstyle W_2 & & % + ... +

    scriptstyle W_n & & & % = 1/n

    scriptstyle D \

    % Matrix/vector row

    begin{bmatrix}

      W_{11} \ W_{12} \ vdots \ W_{1n}

    end{bmatrix}

    & {} + {} &

    begin{bmatrix}

      W_{21} \ W_{22} \ vdots \ W_{2n}

    end{bmatrix}

    & {} + dots + {} &

    begin{bmatrix}

      W_{n1} \ W_{n2} \ vdots \ W_{nn}

    end{bmatrix}

    & {} = {} &

    dfrac{1}{n} &

    begin{bmatrix}

      W_{11} + W_{21} + dots + W_{n1} \

      W_{12} + W_{22} + dots + W_{n2} \

      vdots \

      W_{1n} + W_{2n} + dots + W_{nn}

    end{bmatrix}

  end{array}

]



end{document}

Since scalar multiplication of a vector results in each component being multiplied by the scalar, some simplification in the presentation makes things line up nicely.

A proposition with the mmatrix environment (medium size matrix) from nccmath and cellspace for a proper row spacing:

documentclass{article}

usepackage{amsmath, nccmath}



usepackage[math]{cellspace}

setlength{cellspacetoplimit}{2pt}

setlength{cellspacebottomlimit}{2pt}



newenvironment{bmmatrix}{begin{bmatrix} begin{mmatrix}}{end{mmatrix}end{bmatrix}}

begin{document}



begin{alignat}{3}

begin{matrix}

W_1 \

   begin{bmmatrix}

           W_{11} \

           W_{12} \[-1.5ex]

           vdots \

           W_{1n}

   end{bmmatrix}

end{matrix} &+ &

begin{matrix}

W_2 \

begin{bmmatrix}

           W_{21} \

           W_{22} \[-1.5ex]

           vdots \

           W_{2n}

       end{bmmatrix}

end{matrix}

   &+ hdots{}

   &

+ begin{matrix}

W_n \

begin{bmmatrix}

           W_{n1} \

           W_{n2} \[-1.5ex]

           vdots \

           W_{nn}

end{bmmatrix}

end{matrix}

   &=

begin{matrix}

D \

begin{bmatrix}

           mfrac{W_{11} + W_{21} + hdots + W_{n1}}{n} \[-1ex]

          smash[b]{ vdots }\[-0.5ex]

           mfrac{W_{1n} + W_{2n} + hdots + W_{nn}}{n}

    end{bmatrix}

end{matrix}

end{alignat}



end{document}