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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