18.700 Fall 2010, Final Exam Solutions

نویسنده

  • TRAVIS SCHEDLER
چکیده

Bonus: This is the unique function on matrices that satisfies multilinearity, alternation, and such that det(I) = 1. Here multilinearity means that the function is linear in each column separately, i.e., it is multiadditive and multihomogeneous: multiadditive means that, if A and B are two matrices which have the same columns except for the k-th column, and C is the matrix which has the same columns except for the k-th column which is the sum of the k-th columns of A and B, then det(C) = det(A)+det(B). Similarly, multihomogeneous means that if A and B are two matrices which are the same except in the k-th column where the k-th column of B is λ times the k-th column of A, then det(B) = λ det(A). Finally, alternation means that, if A is a matrix with two identical columns, then det(A) = 0.

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تاریخ انتشار 2011