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I would like to get my text (actually a matrix) to vertically center itself in its cell. Instead, it centers itself based on where the bottom of the tikz picture in the adjacent cell lies. This adds unnecessary height to a table I would like to eliminate. Is there any way to force the text column to align with the center of the tikz picture or to ignore the tikz picture entirely?

documentclass[12pt]{article}

usepackage{amsmath}

usepackage{tikz}   

newcommand{pic}{

 {centering

begin{tikzpicture}[x=1cm,y=1cm]

    useasboundingbox (0,.5) rectangle (3, -2);

    draw (current bounding box.north east) -- (current bounding box.north west) -- (current bounding box.south west) -- (current bounding box.south east) -- cycle;

    end{tikzpicture}}

}



begin{document}

begin{tabular}{| c | c | c |} hline

Initial Pic             &   Final Pic & U \ hline

pic    &   pic    & \ hline

pic    &   pic    &                   $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

pic    &   that    &

                                        $text{U} = .5 begin{bmatrix}

                                            0 & 0 & 0 & 0 \

                                            0 & 0 & 0 & 0 \

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

this    & that      &               $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

end{tabular}                                           

end{document}

You can use baseline=(current bounding box.center) to achieve the desired alignment as shown in the following code:

documentclass[12pt]{article}

usepackage{amsmath}

usepackage{tikz}   

newcommand{pic}{

 {centering

begin{tikzpicture}[x=1cm,y=1cm,baseline=(current bounding box.center)]

    useasboundingbox (0,.5) rectangle (3, -2);

    draw (current bounding box.north east) -- (current bounding box.north west) -- (current bounding box.south west) -- (current bounding box.south east) -- cycle;

    end{tikzpicture}}

}



begin{document}

begin{tabular}{| c | c | c |} hline

Initial Pic             &   Final Pic & U \ hline

pic    &   pic    & \ hline

pic    &   pic    &                   $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

pic    &   that    &

                                        $text{U} = .5 begin{bmatrix}

                                            0 & 0 & 0 & 0 \

                                            0 & 0 & 0 & 0 \

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

this    & that      &               $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

end{tabular}                                           

end{document}

As the border of the image now overlaps with the horizontal lines, you might want to add some extra vertical space (as done here using the cellspace package):

documentclass[12pt]{article}

usepackage{amsmath}



usepackage{cellspace}

setlengthcellspacetoplimit{6pt}

setlengthcellspacebottomlimit{6pt}



usepackage{tikz}   

newcommand{pic}{

 {centering

begin{tikzpicture}[x=1cm,y=1cm,baseline=(current bounding box.center)]

    useasboundingbox (0,.5) rectangle (3, -2);

    draw (current bounding box.north east) -- (current bounding box.north west) -- (current bounding box.south west) -- (current bounding box.south east) -- cycle;

    end{tikzpicture}}

}



begin{document}

begin{tabular}{| Sc | Sc | Sc |} hline

Initial Pic             &   Final Pic & U \ hline

pic    &   pic    & \ hline

pic    &   pic    &                   $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

pic    &   that    &

                                        $text{U} = .5 begin{bmatrix}

                                            0 & 0 & 0 & 0 \

                                            0 & 0 & 0 & 0 \

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

this    & that      &               $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

end{tabular}                                           

end{document}

A fix with an optional argument for the baseline of the tikzpicture:

documentclass[12pt]{article}

usepackage{amsmath}

usepackage{tikz}   

newcommand{pic}[1][-17pt]

 {centering

begin{tikzpicture}[x=1cm,y=1cm,baseline=#1]

    useasboundingbox (0,.5) rectangle (3, -2);

    draw (current bounding box.north east) -- (current bounding box.north west) -- (current bounding box.south west) -- (current bounding box.south east) -- cycle;

    end{tikzpicture}%

}



begin{document}

begin{tabular}{| c | c | c |} hline

Initial Pic             &   Final Pic & U \ hline

pic    &   pic    & \ hline

pic    &   pic    &                   $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

pic[-25pt]    &   that    &

                                        $text{U} = .5 begin{bmatrix}

                                            0 & 0 & 0 & 0 \

                                            0 & 0 & 0 & 0 \

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

this    & that      &               $text{U} = begin{bmatrix}

                                            1 & i & 1 & -i \

                                            -i & 1 & i & 1 \

                                            1 & -i & 1 & i \

                                            i & 1 & -i & 1 end{bmatrix}$ \ hline

end{tabular}                                           

end{document}