A Primary matrix
MATHEMATICS STUDIO V2.0
Vector & Matrix Calculator
From matrix inverses to vector projections: calculate precisely, explore visually, and export your work in seconds. No account or upload.
YOUR WORKSPACE
Vector & Matrix Calculator
01 / INPUT
Build your matrices
Enter numbers, decimals, scientific notation, or fractions like 3/4. Paste entire tables with Import.
B Secondary matrix / RHS
02 / CALCULATE
Matrix operations
For A × B, A columns must match B rows.
01 / INPUT
Explore vectors
Change any component to immediately update the geometric view. Use 2D or 3D coordinates.
Vector APrimary
Vector BReference
02 / CALCULATE
Vector operations
Projection splits A into parallel and perpendicular components relative to B.
03 / RESULT
Calculation result
Your answer appears here
Choose an operation, enter values, and click Calculate result.
04 / EXPLORE
Interactive visualization
The matrix heatmap updates with your last calculation; hover a cell to inspect it.
3D: drag or use arrow keys to rotate · Use the zoom slider to scale.
REVISIT
Recent calculations 0
Your latest calculations will appear here during this session.
Numerical results use double-precision floating point. Matrix scaling improves stability but is not arbitrary precision; high estimated condition numbers trigger a caution. The calculator is not suitable as the sole verification for safety-critical engineering or research calculations.
HOW IT WORKS
One calculator. Two ways to think.
Bring numerical algebra and geometric intuition together, without installing software.
Matrix analysis
Multiply, invert, row-reduce, calculate determinants and eigenvalues, or solve simultaneous equations with clear dimension checks.
Vector geometry
Study dot and cross products, directions, angles, and projections in a responsive plot you can rotate and zoom.
Save and continue
Export results, use a matrix answer as a new input, save/reopen a workspace JSON file, and revisit session history without uploading data.
HELP & LIMITS
Frequently asked questions
What size matrices are supported?
Matrix input is limited to 1×1 through 6×6, with A and B dimensions individually adjustable. Rectangular matrices work for multiplication, addition, subtraction, rank, transpose, row reduction, and compatible systems. Determinants, inverses, traces, and eigenvalues require square matrices.
Can I calculate eigenvalues for non-symmetric matrices?
Yes, for 2×2 and 3×3 real matrices, including complex eigenvalue pairs. For symmetric real matrices, the calculator supports up to 6×6 and can calculate orthonormal eigenvectors. General non-symmetric matrices larger than 3×3 are not supported.
What does AX = B support?
B can have one or more right-hand-side columns. The calculator detects unique, inconsistent and infinitely many solution cases. When solutions are not unique, it returns a particular solution and a nullspace basis so you can express the full solution family.
How accurate are the calculations?
Results are computed with double-precision floating-point arithmetic. Operations on nearly singular matrices, extremely large numbers, or repeated eigenvalues can be numerically unstable. Displayed precision is a rounded presentation and does not imply exact symbolic mathematics.
Does the calculator send my data anywhere?
No. Input values, calculations, plots and in-session history remain in this browser tab. The calculator does not upload information or load third-party computation libraries.