Non-Linear Transformations

Definition

1. Matrix Exponentiation:

   • Raising a matrix to a power greater than one, as in �2A2 or ��An, is not a linear transformation. The composition of linear transformations is not equivalent to matrix exponentiation.

2. Matrix Logarithm:

   • Taking the logarithm of a matrix, denoted as $\log (\mathbf{A})$, is not a linear transformation. The composition of linear transformations is not equivalent to matrix logarithm.

3. Element-Wise Operations:

   • Operations that apply nonlinear functions element-wise to the matrix entries, such as taking the square root or applying trigonometric functions to individual elements, are not linear transformations.