Notations
=========

.. csv-table::

    ":math:`{[K]}_{{N}_{t}\times {N}_{t}}` ", "Stiffness matrix containing dualized boundary conditions"
    ":math:`{[A]}_{N\times N}` ", "Problem stiffness matrix without boundary conditions"
    ":math:`{[B]}_{{N}_{b}\times N}` ", "Boundary condition definition matrix or "constraint matrix""
    ":math:`{[{I}_{d}]}_{{N}_{b}\times {N}_{b}}` ", "Identity matrix of size :math:`{N}_{b}\times {N}_{b}`"
    ":math:`{[Z]}_{N\times {N}_{l}}` ", "Matrix containing a core base (:math:`\mathit{Ker}`) of :math:`B`"
    ":math:`\{u{\}}_{N\times 1}` ", "Vector of travel solutions"
    ":math:`\{{u}_{0}{\}}_{{N}_{b}\times 1}` ", "Vectors of imposed movements"
    ":math:`\{{u}_{N}{\}}_{{N}_{l}\times 1}` ", "Form functions that verify boundary conditions"
    ":math:`({\mathrm{\omega }}_{0},\{\mathrm{\varphi }{\}}_{{N}_{l}\times 1})` ", "Clean modes verifying boundary conditions"
    ":math:`\{f{\}}_{N\times 1}` ", "Imposed load vector"
    ":math:`\{\mathrm{\lambda }{\}}_{{N}_{c}\times 1}`, :math:`\{{\mathrm{\lambda }}_{1}{\}}_{{N}_{c}\times 1}`, :math:`\{{\mathrm{\lambda }}_{2}{\}}_{{N}_{c}\times 1}` ", "Vectors of Lagrange multipliers"
    ":math:`N` ", "Number of degrees of freedom of the unconstrained problem"
    ":math:`{N}_{b}` ", "Number of constraints"
    ":math:`{N}_{t}` ", "Total number of unknowns
    * :math:`N+{N}_{b}` for a simple dualization,
    * :math:`N+2{N}_{b}` for double dualization,"
    ":math:`{N}_{l}` ", "Number of independent unknowns is also the size of the core of :math:`B`
    :math:`{N}_{l}=N-{N}_{b}`"