Matrix Trace Calculator

About this calculator

The trace of a square matrix is simply the sum of the entries on its main diagonal. For a 2×2 matrix with entries a, b, c, d arranged as [[a, b], [c, d]], the trace is a + d, while the determinant, ad − bc, measures how the matrix scales area.

Together, trace and determinant summarise a lot about a matrix's behaviour without needing to fully diagonalise it: for a 2×2 matrix, the trace equals the sum of its two eigenvalues and the determinant equals their product, so these two numbers alone are enough to find the eigenvalues by solving a simple quadratic equation. This makes trace and determinant everyday tools in linear algebra courses, in physics and engineering for analysing linear transformations and stability of systems, and in computer graphics for understanding what a transformation matrix does to shapes.

Enter a 2×2 matrix and this calculator computes both its trace and its determinant.