Traço de Matriz

The matrix trace calculator computes the sum of the diagonal elements of a square matrix. The trace, denoted tr(M), is a fundamental operation in linear algebra, with applications in physics, engineering, and data science. The formula is simple: tr(M) = Σ mᵢᵢ, where mᵢᵢ are the elements at position (i,i) of the matrix.

To use the calculator, enter the matrix elements row by row, separating numbers by commas or spaces. The tool accepts square matrices of any order (2x2, 3x3, etc.). The result is displayed instantly. It is useful for checking manual calculations, especially in problems involving eigenvalues, as the trace equals the sum of the eigenvalues.

Common use cases include: verifying matrix properties in linear transformations, calculating tensor invariants in physics, or simplifying expressions in computer graphics. Caution: the matrix must be square; otherwise, the trace is not defined. Also, note that the trace is linear and invariant under cyclic permutations, but not under arbitrary transformations.

To avoid errors, ensure the matrix is well formatted. Use dots as decimal separators if needed. The calculator does not support symbolic variables, only real numbers. If you need to compute the trace of a matrix product, remember that tr(AB) = tr(BA), but tr(ABC) = tr(BCA) = tr(CAB).