Category
page 1Theorems in linear algebra
Cramer's rule
theorem of solving a system of linear equations
Cayley–Hamilton theorem
theorem that a square matrix satisfies its own characteristic equation
Rouché–Capelli theorem
theorem in linear algebra that a system of linear equations with n variables has solution(s) iff the rk(A) = rk([A|b]), and that if there are solutions, they form an affine space of dimension n−rk(A)
Sylvester's law of inertia
theorem of matrix algebra of invariance properties under basis transformations
spectral theorem
theorem
rank–nullity theorem
theorem
Perron–Frobenius theorem
theorem
Pohlke's theorem
theorem in descriptive geometry
Principal axis theorem
the principal axes an ellipsoid or hyperboloid are perpendicular
dimension theorem for vector spaces
all bases of a vector space have equally many elements
Schur–Horn theorem
characterizes the diagonal of a Hermitian matrix with given eigenvalues
Weinstein–Aronszajn identity
For two suitable matrices, A and B, I+AB and I+BA have the same determinate