的意思 unitary matrix

1. A unitary matrix is a square matrix whose conjugate transpose is its inverse.
一个单位矩阵是一个其共轭转置等于其逆矩阵的方阵。

2. Unitary matrices are commonly used in quantum mechanics to represent transformations of quantum states.
单位矩阵常用于量子力学中表示量子态的转换。

3. The set of all unitary matrices forms a group under matrix multiplication.
所有单位矩阵构成一个矩阵乘法下的群。

4. Unitary matrices preserve the inner product of vectors, ensuring that the norm of a vector remains unchanged.
单位矩阵保持向量的内积，确保向量的范数保持不变。

5. The eigenvalues of a unitary matrix have magnitude 1, since unitary matrices preserve the length of vectors.
单位矩阵的特征值的模为1，因为单位矩阵保持向量的长度。

6. To check if a matrix is unitary, one can verify that its columns form an orthonormal basis and its determinant is a complex number of unit magnitude.
要检查一个矩阵是否是单位矩阵，可以验证其列组成一个正交归一基，并且其行列式是一个单位模的复数。