3阶实方阵的实正交-对称和分解

对于任意3阶实方阵A=(a

Sum decomposition of three order real square matrix

This article comes to the conclusion that three order reqular intersection real square matries can be decomposed into the product of a regular intersection real square matrix and a real symmetric square matrix.It is proved by the sum decomposition of non-symmetric real square matrix that to an arbitrary three order real square matrix A=(aij)3×3,recorded as Δ=(a12-a21)2 +(a13-a31)2+(a23-a32)2,the regular intersection real square matrix B and the symmetric real square matrix C can exist. When Δ≤4, we can get A=B+C, just |B|=1; When Δ>4,the real number α=tΔ(t≥1)can exist,then we can get A=α(B+C), just |B|=1.