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\documentclass[12pt,letterpaper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\begin{document}
Ugly alignment :
\begin{equation}
X =
\begin{bmatrix}
x & y
\end{bmatrix}\!\!
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}\!\!
\begin{bmatrix}
x \\
y
\end{bmatrix}
\end{equation}
\end{document}
Is there a way to draw that left matrix properly vertically aligned with the top part of the middle matrix ? How can I add a proper vertical offset ?
Also, I don't like the items spacement inside the matrices. I can adjust the spacements by adding some \phantom commands, but it feels like an hack. What do you suggest ?