Confusing about linearity and nonlinearity

[KFC]

Hi there, in the course of linear algebra, we talk about many on matrix and related properities. I wonder if any equations written in terms of matrices are linear? Could nonlinear equations also written in matrices?

Thanks

 

[g_edgar]

Suppose $A$ is an $n \times n$ matrix and $\mathbf{x}$ is $n \times 1$. Then: $\mathbf{x}^{T} A \mathbf{x}$ is a quadratic form in $\mathbf{x}$

 

[John Creighto]

Hi there, in the course of linear algebra, we talk about many on matrix and related properities. I wonder if any equations written in terms of matrices are linear? Could nonlinear equations also written in matrices?

Thanks

Take any function, and express it as a taylor series. Replace x with Ax and you got a non linear function expressed in terms of matrices.