Trace of a 2x2 Matrix

The Trace of a 2x2 Matrix calculator compute the Trace of a 2x2 matrix.

INSTRUCTIONS: Enter the following:

• (A) This is the 2x2 matrix

TRACE: The calculator returns the trace of the 2x2 matrix.

The Math

The trace of an nxn matrix A is the sum of the diagonal entries `A_11, A_22,...,A_(n n)`. So `"tr"(A)=sum A_(ii)`.

For the 2x2 matrix
`A = [[A_11 , A_12], [A_21 , A_22]]`,
the trace is given by `A_11 +A_22`.

The trace of a matrix is useful in determining the eigenvalues (`λ_i`) of the matrix. For any matrix, `sum λ_i= sum A_(ii) ="tr"(A)`. 

2x2 Matrix Calculators :

• To compute the Characteristic Polynomial of a 3x3 matrix,CLICK HERE.
• To compute the Determinant of a 2x2 Matrix, CLICK HERE.
• To compute the Inverse of a 2x2 Matrix, CLICK HERE.
• To compute the Eigenvalues of a 2x2 Matrix, CLICK HERE.
• For the Classifying Equilibria of a 2x2 Matrix, CLICK HERE.
• To compute the Eigenvalues and Eigenvectors of a 2x2 Matrix, CLICK HERE.
• To multiply a 2x2 matrix by a scalar, CLICK HERE.
• To compute the Characteristic Polynomial of a 2x2 Matrix, CLICK HERE.