algebra

What I do

• Solve equations and polynomial roots
• Factor expressions and find greatest common divisors
• Work with matrices and linear transformations
• Apply group, ring, and field theory
• Analyze vector spaces and basis transformations
• Solve systems of linear equations

When to use me

When solving mathematical problems, working with abstract algebraic structures, or optimizing linear systems.

Key Concepts

• Quadratic Formula: x = (-b ± √(b²-4ac))/2a for ax² + bx + c = 0
• Matrix Multiplication: (AB){ij} = Σ_k A{ik}B_{kj}
• Determinant: det(A) nonzero implies matrix invertible
• Eigenvalues: Solutions to det(A - λI) = 0
• Group: Set with associative binary operation, identity, inverses
• Field: Commutative ring where nonzero elements form group