The
nullity of the matrix A is 2, indicating that it has two linearly dependent columns.
矩阵A的零性为2,表明它有两列线性相关。
In this case, the
nullity of the transformation T is 1, meaning there's only one direction in which vectors can be mapped to zero.
在这种情况下,变换T的零性为1,这意味着只有单一的方向可以使向量映射为零。
The
nullity of the differential operator D on the space of smooth functions is zero because every function in this space is mapped to itself.
在光滑函数空间上微分算子D的零性为零,因为这个空间中的每一个函数都被映射到自身。
When calculating the
nullity of a linear transformation, one must consider both its kernel and image dimensions.
计算线性变换的零性时,需要考虑其核和像的维度。
The
nullity of the matrix representing the system of linear equations is zero, implying the system has a unique solution.
表示线性方程组的矩阵的零性为零,意味着该系统有一个唯一的解。
In the context of electrical circuits, the
nullity of a circuit refers to the number of independent loops in the circuit diagram.
在电气电路的背景下,电路的零性指的是电路图中独立回路的数量。
The
nullity of the adjacency matrix of a graph is equal to the number of connected components minus one if the graph is not complete.
图的邻接矩阵的零性等于图的连通分量数减一,如果图不是完全图的话。
For a given linear transformation, if the
nullity is equal to the dimension of the domain, the transformation is considered trivial.
对于给定的线性变换,如果零性等于域的维数,则认为变换是平凡的。
In quantum mechanics, the
nullity of an operator can indicate the degeneracy of energy levels within a system.
在量子力学中,操作符的零性可以指示系统内部能级的退化程度。
When analyzing the stability of a dynamical system, the
nullity of the Jacobian matrix at a critical point can provide insights into the system's behavior near that point.
在分析动力系统的稳定性时,关键点处雅可比矩阵的零性可以提供关于系统在该点附近的动态行为的见解。
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