By using the Gram matrix of vector group, the definition of the degree of linear independence of vector group in the Euclid space was given. Some properties are deduced. The distance formula from a vector to a subspace and the error formula of the least square solution of non-homogeneous linear equation were both presented in the form of the degree of linear independence. Accordingly, the hnear expression with minimum error can be determined for a smaller degree of the linear independence of vector group. A practical example showed that the most important vector can be c...
