# General definition for higher order co-moment matrix

Is there a general equation or procedure for computing higher-order co-moment matrices (i.e., coskewness matrix, cokurtosis matrix, etc) for a vector of random variables?

For example, the covariance matrix of a vector of random variables $$\mathbf{X} = (X_1, ..., X_N)$$ is an $$N \times N$$ matrix $$\mathbf{C}(\mathbf{X})$$ defined by

$$\mathbf{C}(\mathbf{X}) = \mathrm{E}\big[(\mathbf{X}-\mathrm{E}[\mathbf{X}])(\mathbf{X}-\mathrm{E}[\mathbf{X}])^\top \big]$$

Which can be written equivalently as:

$$\mathbf{C}(\mathbf{X}) = \mathrm{E}[\mathbf{X}\mathbf{X}^\top]-\mathrm{E}[\mathbf{X}]\mathrm{E}[\mathbf{X}]^\top$$