3x3 Matrix Explorer

The transpose of a matrix A is a matrix (A^T) whose (i^th) column is equal to the (i^th) row of A.

The inverse of a 3×3 matrix A is a matrix (A^(-1)) such that A (A^(-1)) 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 A x=b 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 λ is an eigenvalue of A if there is some nonzero vector x such that A x=λ x; the vector x is called an eigenvector. In the result, the (i^th) row of the eigenvector array is an eigenvector of unit length associated with the (i^th) eigenvalue in the eigenvalue array.

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Contributed by: Chris Boucher

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