All Questions

Given $c\in\Bbb R^{n_1},d\in\Bbb R^{n_2}$, $E\in\Bbb R^{n_1\times n_2}$, $A\in\Bbb R^{m_1\times n_1}$, $B\in\Bbb R^{m_2\times n_2}$ $a\in\Bbb R^{m_1}$, $b\in\Bbb R^{m_2}$ and $t\in\Bbb R$ we know ...

Is there any fast algorithm that output an orthogonal basis $e_i,i\leq n$ of $R^n$ with $e_i\in V_i$? Where $V_i,i\leq n$ are given linear subspaces of $R^n$. And is there any condition on $V_i,i\leq ...