正交矩阵与其应用 毕业论文.doc

本科生毕业设计（论文） 正交矩阵与其应用 (The orthogonal matrix and its applicalion) 学 院： 专 业： 学 号： 学生姓名： 指导教师： 二〇一 年 六 月 摘 要 正交矩阵是实数特殊化的酉矩阵，因此总是正规矩阵。尽管我们在这里只考虑实数矩阵，这个定义可用于其元素来自任何域的矩阵。正交矩阵毕竟是从内积自然引出的，对于复数的矩阵这导致了归一要求。要看出与内积的联系，考虑在n维实数内积空间中的关于正交基写出的向量。的长度的平方是。如果矩阵形式为 的线性变换保持了向量长度，所以有限维线性等距同构，比如旋转、反射和它们的组合，都产生正交矩阵。反过来也成立:正交矩阵蕴涵了正交变换。但是，线性代数包括了在既不是有限维的也不是同样维度的空间之间的正交变换，它们没有等价的正交矩阵。有多种原由使正交矩阵对理论和实践是重要的。正交矩阵形成了一个群，即指示为的正交群，它和它的子群广泛的用在数学和物理科学中。使得它在不同的领域都有着广泛的作用,也推动了其它学科的发展。 本文从以下主要例举了正交矩阵的三大应用:正交矩阵在线性代数中的应用、正交矩阵在化学中的应用、正交矩阵在物理中的应用。 关键词: 正交矩阵;酉矩阵;正交群;正交变换 Abstract The orthogonal matrix and its applicalion Orthogonal matrix is a real specialization of the unitary matrix, it is always normal matrix. Although we here consider only real matrices, this definition can be used from any domain in its matrix elements. Orthogonal matrix , after all, the inner product of the natural leads, and the complex matrix that led to the normalization requirements. To see the link with the inner product, consider the n-dimensional real inner product space to write on the orthogonal basis vector . the length of the square is . If the matrix form of linear transformation maintained vector length, then Therefore finite-dimensional linear isometry, such as rotation, reflection, and their combination, have generated orthogonal matrix. In turn, set up: orthogonal matrix implies the orthogonal transformation. However, linear algebra, including finite-dimensional in neither the same nor is the dimension of the space between the orthogonal transformation, they are not equivalent orthogonal matrix. There are many Reasons to orthogonal matrix theory and practice is important. orthogonal matrices form a group that is directed to the orthogonal group,which is indicated ,it and its subgroups widely u