  The Kalman canonical form for quantum linear systems was derived in
\cite{ZGPG18}. The purpose of this paper is to present an alternative
derivation by means of a Gramian matrix approach. Controllability and
observability Gramian matrices are defined for linear quantum systems, which
are used to characterize various subspaces. Based on these characterizations,
real orthogonal and block symplectic coordinate transformation matrices are
constructed to transform a given quantum linear system to the Kalman canonical
form. An example is used to illustrate the main results.
