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Interactive mathematical studio exploring 2D linear transformations, determinants, eigenvalues/eigenvectors, dot/cross products, and linear systems solver.
Visualize basis vectors (î, ĵ), grid deformation, rotation, reflection, and shear in real-time animation.
Computes Determinant, Trace, Rank, Eigenvalues, and Inverse Matrix (A⁻¹) with step-by-step clarity.
Analyze dot products, projections, vector angles, and solve 2x2 linear systems via Cramer's rule.
• Determinant: Det(A) = ad - bc • Trace: Tr(A) = a + d • Characteristic Eq: λ² - Tr(A)λ + Det(A) = 0 • Dot Product: u · v = |u||v|cos(θ) = u₁v₁ + u₂v₂ • Cramer's Rule: x = Det(Dx) / Det(D), y = Det(Dy) / Det(D)
A determinant of 0 indicates that the 2D space has collapsed into a 1D line or 0D point, losing all area information, meaning the transformation cannot be inverted (singular matrix).
Interactive 118 chemical elements with real-time temperature state simulation, Bohr orbitals, and chemistry quiz.
Interactive multiplication tables from 1x1 to 19x19, custom N-dan generator, dot area model, and mental math quiz.
Interactive Unit Circle visualizer, sine/cosine/tangent wave graphs, triangle solver, and speed math quiz.
Interactive hierarchy of numbers (Natural, Integer, Rational, Irrational, Real, Complex) and historical invention motives.