Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and sufficient conditions for regularity of interval parametric matrices in terms of boundary parametric hypersurfaces, parametric solution sets, determinants, real spectral radiuses. The initial n-dimensional problem involving K interval parameters is replaced by numerous problems involving 1<= t <= min(n-1, K) interval parameters, in particular t=1 is most attractive. The advantages of the proposed methodology are discussed along with its application for finding the interval hull solution to interval parametric linear system and for determining the regularity radius of an interval parametric matrix.

翻译：用于检查间距参数矩阵正常度的充足条件通常在大的参数间隔下失效。我们为间距参数矩阵的正常度提供了必要和充分的条件,从边界参数超表层、参数溶液组、决定因素、真实的光谱半径来看,我们为间距参数矩阵的正常度提供了必要和充分的条件。涉及K间距参数的初始正维问题被涉及1 ⁇ t ⁇ min(n-1,K) 间距参数的许多问题所取代,特别是t=1, 最有吸引力。我们讨论了拟议方法的优点,同时讨论了对间距线性系统寻找间距船体解决方案和确定间距参数矩阵的正常度。