A new spectral approach in the matrix algebra: $\mathrm{C}$-determinant pseudospectrum

We develop a general framework for perturbation analysis of matrix. More specifically, the $\mathrm{C}$-determinant pseudospectrum $\mathrm{Det}_{\varepsilon}^{C}(T)$ for an element in the matrix algebra $\mathcal{M}_n(\mathbb{C})$ is studied. We also make several observations on the $\mathrm{C}$-determinant pseudospectrum.