The Almost Orthogonal Matrix and Almost Symmetric Matrix

Use of sub-transposed matrix to have given the concepts of almost orthogonal matrix and almost (anit-)symmetric matrix, and their basic properties and relations is discussed, and many new re- sults have been obtained, orthogonal matrix and symmetric matrix and anit- symmetric matrix between of corresponding result have been popularized, especially orthogonal matrix's Cayley decomposition is extended into almost orthogonal matrix fields, and various kind orthogonal matrix and symmetric ma- trix and generalized inverse matrix is unified.