| 1. | The speed of light is an invariant constant .
光速是一个不变常数。 |
| 2. | The first invariant of strain is independent of the coordinate system being used .
第一应变不变量与所用的坐标系无关。 |
| 3. | In other words, the hermiticity of a matrix is invariant under unitary transformations .
换言之，矩阵的厄密性在幺正变换下保持不变。 |
| 4. | For a system, hamiltonian is invariant under any translation of spatial coordinates .
对于一体系，哈密算符在任何空间坐标变换下是不变的。 |
| 5. | One could consider invariant properties of figures under each of the above types of transformation .
可以在上述的每一类型变换下考虑图形的不变性质。 |
| 6. | Since scalars are independent of the coordinate system, the dot product of two vectors is called a scalar invariant .
因为标量与坐标系无关，故两个矢量的点积称为标量不变量。 |
| 7. | Finally, since there is no absolute origin in time, all systems must be invariant under time displacements .
最后，因为没有绝对的时间原点，所以任何系统在时间平移下一定不变。 |
| 8. | One of the most important, most difficult, and most exasperating unsolved problems of operator theory is the problem of invariant subspaces .
算子理论中最重要、最困难也最令人烦恼的未解决问题之一就是不变子空间问题。 |
| 9. | Between these two extremes there are the questions for which the answers are invariant under change of dimension, but the techniques are not .
在这两个极端之间还有这样的问题，当维数改变时它们的解答不变，但（证明的）技巧则不然。 |
| 10. | The cheapest way to get one is to invoke the spectral theorem and to conclude that normal operators always have non-trivial invariant subspaces .
取得这样结果的最省力的尝试是引用光谱定理而得到正规算子恒有非平凡不变子空间的结论。 |
