App Linear Algebra for Android

Linear algebra calculator with **exact arithmetic** (common fractions with BigInteger) and **step-by-step** solutions. Languages: English (basic), Bulgarian, German, French and Spanish – switchable from the menu, regardless of the device language.

## Operations
- A + B, A − B, A B, k A, Aᵀ, tr(A), Aᵏ (incl. negative powers)
- det(A) – triangularization, with any elementary transformation
- A⁻¹ – Gauss–Jordan on [A | I], with verification A·A⁻¹ = I
- rank(A) and RREF (Gauss–Jordan method), leading pillars
- System A x = b – unique solution / infinite (parametric and vector form) / incompatible (Kronecker–Cappelli)
- LU decomposition P·A = L·U
- Characteristic polynomial (Fadeev–Lövrier), eigenvalues ​​(exact rational, square radicals, numerically complex), eigenvectors, multiplicities, diagonalizability
- Kernel, image and space of rows (basis, rank theorem)
- Gram–Schmid: orthogonal and orthonormiran basis
- Vectors u, v: scalar and cross product, lengths, angle, distance, projections, parallelogram face, orthogonality/collinearity

Input: `3`, `-2/5`, `0.75`, `1.5` (empty cell = 0). The maximum size (2…20, default 10) is set in **Settings**.

## Parameter in elements
Cells can contain a parameter (the letter is selected in Settings, by default `a`): `2a+1`, `a^2-1`, `(a+1)(a-2)`, `1/(a-1)`.
- **det(A)** – as a polynomial factored; at which values ​​A is invertible.
- **rank(A), RREF** – general case + special values ​​with their rank.
- **A⁻¹** – with rational functions and a validity condition.
- **System A x = b** – full study: general case (solution as a function of the parameter) and each special case separately (incompatible / unique / countless solutions).
- +, −, ·, k·A (k may contain the parameter), Aᵀ, tr, Aᵏ.
For other operations (eigenvalues, LU, Gram–Schmitt…) enter a specific value in the "Parameter value" field.
The calculations run in a background thread. The "Result → A" button transfers the matrix result for the next operation.