Important conclusions of Gram determinants in Euclid space;

By using the co-ordinate transform between the general base and the orthogonal base of the Euclid space, the current signal is decomposed to a series of orthogonal currents including a broad-sense fundamental current and a harmonic current.

By the relation transvection,we obtain two necessary and sufficient conditions for the transformation being linear transformation in Euclid spaces,and out of it,we have got some conclusions.

On distance between a p-dimensional plane and a q-dimensional plane in Euclidean space E~n;

Curvature and geometric property of submanifolds in Euclidean spaces;

Generalized normal operator and generalized normal matrix on the general Euclidean space;

Arnheim’s architecture space idea focuses attention on the perception characters of architecture space, emphasizes on whole architecture space imagine, explains architecture space implication with visual dynamics.