Matrix operations - Matrix calculations & solutions

This matrix calculator offers a variety of operations, including:

- Solving systems of linear equations through:

★ Gaussian elimination

★ Cramer's rule

★ Gauss-Jordan elimination

★ The inverse matrix method

★ Montante (also known as Bareiss algorithm)

- Calculating the determinant of a matrix using:

★ Decomposition method

★ Triangular form reduction

★ Montante (Bareiss algorithm)

★ Sarrus' rule (applicable to 3x3 matrices only)

- Determining the inverse of a matrix via:

★ Gaussian elimination

★ Gauss-Jordan elimination

★ Algebraic complements

★ Montante (Bareiss algorithm)

- Assessing the rank of a matrix using:

★ Elementary transformations

★ Bordering minors

- QR decomposition methods such as:

★ Gram–Schmidt process

★ Householder reflections

★ Givens rotation

- Polar decomposition;

- Calculating the square root of a matrix;

- Singular value decomposition;

- Finding eigenvalues

- Finding eigenvectors

- Performing eigendecomposition (matrix diagonalization);

- Identifying matrix minor;

- Identifying matrix cofactor;

- Finding the adjoint of a matrix;

- LU decomposition;

- Schur decomposition;

- Cholesky decomposition;

- Solving matrix equations;

- Raising matrices to a power;

- Scaling a matrix by a constant;

- Transposing a matrix;

- Matrix multiplication;

- Matrix subtraction;

- Matrix addition;

Application Features:

- Customized keyboard for easier data entry;

- Detailed step-by-step solutions;

- Option to save solutions;

- Capability to edit saved solutions;

- Offline functionality;

- Displaying solutions in both ordinary and decimal fractions.

Review: Matrix Calculator Pro - The Computational Powerhouse That Transforms Abstract Math into Elegant Clarity

As an engineering student drowning in linear algebra, this app didn’t just simplify matrices—it demystified them. The moment I fed it a messy 4x4 system, its step-by-step Gaussian elimination breakdown felt like a patient tutor illuminating every pivot and row operation. Need to check my Cholesky decomposition? The app’s detailed trace proved invaluable. But where it truly excels is adaptability: swapping between exact fractions and decimals mid-calculation preserved precision during eigenvalue checks, while the custom matrix keyboard made inputting symbolic matrices surprisingly fluid. 

Offline functionality rescued me during a cross-country flight—comparing QR decomposition methods (Householder vs. Givens) without Wi-Fi highlighted subtle stability differences. Beyond solving, it’s a discovery tool: visualizing eigenvector directions alongside singular values transformed abstract concepts into intuitive insights. For educators, researchers, or anyone wrestling with multidimensional data, this isn’t a calculator—it’s a revelation wrapped in minimalist design.

Frequently Asked Questions (FAQs):

Q: How accurate are solutions for ill-conditioned matrices or near-singular systems?

A: Impeccable precision. The app employs scaled pivoting in Montante’s method to mitigate rounding errors. For near-singular cases, it warns of high condition numbers and suggests regularization or SVD alternatives.

Q: Can it handle complex-number matrices or only real entries?

A: Currently supports real numbers only. Complex matrix operations (e.g., Hermitian decompositions) are not included—stick to real eigenvalues and real-valued systems.

Q: Is there a size limit for matrices?

A: Performance-based: Up to 10x10 runs smoothly on most devices. Larger systems (15x15+) may lag slightly but remain functional. Avoid gigantic matrices (50x50+) without GPU support.

Q: How does "saving solutions" work? Can I export to LaTeX/MATLAB?

A: Saved solutions store locally with timestamps. Export supports plain text or PDF (with matrix notation). LaTeX/MATLAB export isn’t native but copy-paste adapts well to most editors.

Q: Does the step-by-step mode show every intermediate matrix?

A: Toggle detail depth: "Concise" shows key steps (row ops, pivots); "Verbose" displays every intermediate matrix, ideal for debugging homework proofs.

Q: Can I compute matrix functions (e.g., eᴬ, sin(A))?

A: Beyond powers/scaling? No. Focus is on decompositions, inverses, and linear systems—not transcendent matrix functions. Use specialized tools for those.

Q: Why choose this over Wolfram Alpha or MATLAB Mobile?

A: Offline freedom, zero subscription cost, and pedagogical step-by-step guidance. Tailored for learners needing clarity over raw computational power.