This calculator finds several key properties of a square matrix.

Determinant: A scalar value that provides important information about the matrix. A non-zero determinant means the matrix is invertible.

Trace: The sum of the elements on the main diagonal (from the top left to the bottom right).

Rank: The maximum number of linearly independent column (or row) vectors in the matrix. It is found by reducing the matrix to row echelon form and counting the number of non-zero rows.

Norms: A measure of the "size" or "length" of a matrix.

• L1 Norm: The maximum of the column sums of the absolute values of the elements.
• Infinity Norm: The maximum of the row sums of the absolute values of the elements.
• Frobenius Norm: The square root of the sum of the absolute squares of its elements.