Linear algebra
Linear algebra calculators
Matrices, determinants, systems of equations and eigenvalues: the tools of a linear algebra course, with the intermediate results in plain view.
Which calculation you need
Matrices and vectors is the general workbench: sums, products, transposes and dot products between two matrices you can keep open side by side. The determinant is the number that says whether a square matrix is invertible: if it is zero the matrix is singular, and the calculator also shows the rank and the inverse where one exists. The linear systems calculator applies the Rouché-Capelli theorem, comparing the rank of the coefficient matrix with that of the augmented one, and separates the three possible cases: a unique solution, infinitely many, or none at all. Eigenvalues and eigenvectors close the loop: they are the directions the matrix merely stretches, and they underpin diagonalisation, principal component analysis and stability analysis.
Matrices and vectors
Addition, product, determinant, transpose, dot product and magnitude.
Vector mathematics
Magnitude, unit vector, dot and cross products, angle, projection and areas, with a drawing in the plane.
Determinant and inverse
Determinant, rank and inverse of a square matrix, with an invertibility check.
Systems of linear equations
Gauss-Jordan elimination, classification of the system and the general solution.
Eigenvalues and eigenvectors
Characteristic polynomial, real and complex eigenvalues, eigenvectors and trace.