Matrix Calculator

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Perform essential operations on a 2x2 matrix: determinant, trace, and eigenvalues.

Matrix A

Edit matrix elements directly above

Matrix Properties

Determinant-2.0000

Trace5.0000

Eigenvalues5.37, -0.37

About this calculator

Linear Algebra

Linear algebra is the branch of mathematics concerning linear equations and their representations in vector spaces and through matrices. It is central to almost all areas of mathematics.

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Pro Tips

Invertibility: A matrix is invertible if and only if its determinant is non-zero.
Trace: The sum of diagonal elements (a+d).
Eigenvalues: Roots of calculation λ² - tr(A)λ + det(A) = 0.

Fun Facts

"The word 'matrix' was introduced by James Joseph Sylvester in 1850."
"Matrices are used in computer graphics to project 3D images onto a 2D screen."
"Google's PageRank algorithm is based on finding the principal eigenvector."

Formula: det(A) = ad - bc