<正>定义了O-正交矩阵、R-正交矩阵、L-正交矩阵等概念，并分析了右转置矩阵、左转置矩阵和全转置矩阵与正交矩阵的关系，得到正交矩阵的充分必要条件。并给出了（）_正交矩阵、R-iE交矩阵、L-正交矩阵的一些相关结论。

A progeny test analysis was made on the half-Sib opening pollined families of the first batch plus-tree of Liquidambar formosana Hance. The results showed that there was significant genetic variation among the families. The family heritability for height, annual height,diameter, tree crown and branch numbers were 14. 53%～47. 58%, 13. 36%～35. 43%, 6. 40%～37. 04%, 14. 25%～35. 30%, 6. 19%～18. 78%～The individual heritability of height, annual height, diameter,crown of tree and branch numbers were 21. 26%～52. 91%, 16. 97%～28. 63%,13. 23%～22. 22%,18. 76%～30. 69%,9. 03%～15. 58%,respectively. the additive genetic variation coefficient of each trait was 4. 979%～9. 667%, 5. 913%～12. 783%, 5. 164%～6. 731%, 6. 240%～10. 567%, 4. 952%～11. 780%, respectively. And the correlation extent was also significant. The genetic gain of height and diameter of the selected families was estimated,which were 6. 52%～19. 00% and 3, 820～24. 32% respectively.