In　this　paper,　we　introduce　a　geometric　model　for　linear　symmetric　eigenvalue　problem,　which　is　motivated　by　the　fact　that　any　eigenvalue　of　a　symmetric　positive　definite　matrix　A　is　the　reciprocal　of　the　square　length　of　an　axis　of　the　ellipsoid　x(T)　Ax　=　1.　Hence,　to　find　the　largest　eigenvalue　is　equivalent　to　calculate　the　shortest　axis　of　the　corresponding　ellipsoid.　Two　sequential　subspace　projection　algorithms　based　on　this　idea　are　proposed,　and　we　establish　the　global　convergence　and　local　linear　convergence　rate　of　our　proposed　algorithms.　Numerical　experiments　demonstrate　that　our　algorithm　outperforms　the　MATLAB　built-in　solver　＂EIGS＂　which　calls　the　famous　package　＂ARPACK＂.