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Trace of a 2x2 Matrix

$\text{Trace} = A_(11) + A_(22)$

$(A)" 2x2 Matrix"$

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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.