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The transpose of a matrix ... is a matrix ... whose ... column is equal to the ... row of ... . The inverse of a ... matrix ... is a matrix ... such that ... is the identity matrix. The trace of a matrix is the sum of the entries on the main diagonal (upper-left to lower-right). The determinant is computed from all the entries of the matrix and is nonzero precisely when the matrix is nonsingular, that is, when the equation ... always has a unique solution. The matrix rank is the number of linearly independent columns and is equal to three precisely when the matrix is nonsingular. A number ... is an eigenvalue of ... if there is some nonzero vector ... such that ... ; the vector ... is called an eigenvector. In the result, the ... row of the eigenvector array is an eigenvector of unit length associated with the ... eigenvalue in the eigenvalue array.
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