The number of alternating sign matrices is given by the Hankel type of these for binomial coefficients, while the top exterior algebra gives its value for a general linear transformation. This function of the matrix exponential is equal to the exponential of the trace, and it is the unique alternating multilinear function from the space of square matrices to its underlying field. For two vectors in three-space, it can be used as a mnemonic for the value of the cross product, and it is invariant under elementary row and column operations. FTP, give this function that as
The number of alternating sign matrices is given by the Hankel type of these for binomial coefficients, while the top exterior algebra gives its value for a general linear transformation. This function of the matrix exponential is equal to the exponential of the trace, and it is the unique alternating multilinear function from the space of square matrices to its underlying field. For two vectors in three-space, it can be used as a mnemonic for the value of the cross product, and it is invariant under elementary row and column operations. FTP, give this function that associates to each square matrix a scalar and which can be computed by cofactor expansion.
The number of alternating sign matrices is given by the Hankel type of these for binomial coefficients, while the top exterior algebra gives its value for a general linear transformation.
determinant