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The paper is concerned with the following $n\times n$ Dirac typeequation$$Ly=-iB(x)^{-1}(y'+Q(x)y)=\lambda y, \quad B(x)=B(x)^*,\quad y={\rmcol}(y_1,\ldots,y_n),\quad x\in[0,\ell],$$ on a finite interval $[0,\ell]$.Here $Q$ is a summable potential $n\times n$ matrix function and $B$ is aninvertible self-adjoint diagonal bounded matrix function. If $n=2m$ and$B(x)={\rm diag}(-I_m,I_m)$, this equation is equivalent to Dirac equation oforder $n$.  We show the existence of triangular transformation operators for suchequation under additional uniform separation conditions on the entries of thematrix function $B$. Here we apply this result to study direct spectralproperties of the boundary value problem (BVP) associated with the aboveequation subject to the general boundary conditions $U(y)=Cy(0)+Dy(\ell)=0,{\rmrank}(C\ D)=n$.  We apply this result to show that the deviation of the characteristicdeterminants of this BVP and the unperturbed BVP (with $Q=0$) is a Fouriertransform of some summable function, which in turn yields asymptotic behaviorof the spectrum in the case of regular boundary conditions. Namely,$\lambda_m=\lambda_m^0+o(1)$ as $m\to\infty$, where$\{\lambda_m\}_{m\in\mathbb{Z}}$ and $\{\lambda_m^0\}_{m\in\mathbb{Z}}$ aresequences of eigenvalues of perturbed and unperturbed ($Q=0$) BVP,respectively.  Further, we prove that the system of root vectors of the above BVPconstitutes a Riesz basis in a certain weighted $L^2$-space, provided that theboundary conditions are strictly regular.  The main results are applied to establish asymptotic behavior of eigenvaluesand eigenvectors, and the Riesz basis property for the dynamic generator of theTimoshenko beam model. We also found a new case when eigenvalues have anexplicit asymptotic, which to the best of our knowledge is new even in the caseof constant parameters of the model.

On transformation operators and Riesz basis property of root vectors  system for $n \times n$ Dirac type operators. Application to the Timoshenko  beam model