A matrix pencil in mathematics is a linear equation system, which consists of matrices with complex elements
In linear algebra, if $A_{0},A_{1},\dots ,A_{l}$ are ${\displaystyle n\times n}$ complex matrices for some nonnegative integer ${\displaystyle l}$, and ${\displaystyle A_{l}\neq 0}$ (the zero matrix), then the matrix pencil of degree ${\displaystyle l}$ is the matrix-valued function defined on the complex numbers ${\displaystyle L(\lambda )=\sum _{i=0}^{l}\lambda ^{i}A_{i}.}$.
