matrixcalc.org

Open matrixcalc.org, type your numbers into the grid cells for Matrix A (and Matrix B if needed), then click the operation button you want — or type an expression like {{1,2},{3,4}}^-1 into the input field and press Enter. The result appears below with step-by-step solutions for many operations. This works for both square and non-square matrices; leave extra cells empty to define a non-square shape.

Entering matrix elements

The site gives you two ways to get data in:

• Grid entry — Click a cell and type a number. Use ↵ Enter, Space, or the arrow keys to move between cells. Backspace and Delete clear a cell. To build a non-square matrix, just leave the unused cells empty.
• Matrix literal syntax — Type the whole matrix at once in the form {{1,2,3},{4,5,6},{7,2,9}}, where each inner {...} is a row. This is faster for anything larger than 2×2 and avoids clicking cell by cell.

You can paste a matrix from a text editor with Ctrl/Cmd + V, and you can drag a matrix from the results area back into the input (or out to a text editor).

What values are accepted

The input field is not limited to plain integers. According to the site, you can enter:

So if you need an exact fraction or a symbolic entry, you don't have to convert it to a decimal first.

Running calculations

There are two routes, and they produce the same results.

Route 1: Click an operation button

Each matrix panel (A and B) has buttons for the common operations: Determinant, Inverse, Transpose, Rank, Multiply by, Row echelon form, Diagonal matrix, To the power of, LU decomposition, Cholesky decomposition. Between the two panels you'll find the binary operations: A × B, A + B, A − B. Below that are A*X=B and A^-1 for solving systems.

Click the button, and the calculator applies that operation to the matrix you entered.

Route 2: Type an expression

Type the operation directly, using operators + - * / \ ! ^ ^{*} and functions such as:

sqrt, cbrt, exp, log, abs, conjugate, arg, min, max, gcd, rank, adjugate, inverse, determinant, transpose, pseudoinverse, trace, cos, sin, tan, cot, cosh, sinh, tanh, coth, arccos, arcsin, arctan, arccot, arcosh, arsinh, artanh, arcoth, derivative, factor, resultant

For example:

determinant({{1,2,3},{4,5,6},{7,2,9}})
{{1,2},{3,4}}^-1
{{11,3},{7,11}}*{{8,0,1},{0,3,5}}

Press Enter and the result is computed. The site lists these exact examples, so they're a safe way to confirm your syntax is right before trying something more complex.

Reading and formatting the result

• Step-by-step solutions are provided for many operations (the site advertises solution steps alongside determinant, inverse, rank, and system solving).
• Decimal vs. fraction display — There are controls for "Display decimals," "number of fraction digits," and "number of significant digits." Use these when you want an exact fraction instead of a rounded decimal, or when you need to control rounding.
• Cleaning up — The ↶ (undo) and Clean controls reset or step back through your input.

Solving systems of linear equations

For A*X = B, enter the coefficient matrix as A and the constants as B, then use the A*X=B control. The site also supports the Y+A=B form. Because the calculator handles non-square matrices (empty cells), you can set up systems that aren't square, though the solution method and whether a unique solution exists depend on the matrix itself.

Common snags

• Non-square matrices — Don't fill every cell. Empty cells are how the calculator knows the shape is rectangular rather than square.
• Syntax errors in literals — Rows go inside {...}, and the whole matrix is wrapped in another {...}: {{row1},{row2}}. A missing brace is the usual cause of a parse failure.
• Symbolic entries — Expressions like (1+x)/y^2 are accepted, but if x or y aren't defined the result stays symbolic rather than numeric.
• Keyboard navigation — If typing seems to jump cells unexpectedly, you're probably hitting Space or an arrow key, which move the cursor rather than insert a character.

Quick reference

The site also links to Wikipedia for background on matrices if you need to review the underlying concepts before computing.

Matrix Calculator at matrixcalc.org is a browser-based tool for doing linear algebra computations on matrices you type in yourself. It handles the core operations — determinant, inverse, transpose, rank, addition, subtraction, multiplication, and exponentiation — plus matrix decompositions (LU, Cholesky, QR, SVD) and solving systems of linear equations. You enter matrix elements directly, click a button, and get a result; the site also advertises solution steps for systems of linear equations. It's useful when you need a quick numeric or symbolic answer without installing software, and it works with both square and non-square matrices (leave extra cells empty for the latter).

What operations it supports

The calculator groups its functions around two matrices, A and B, with a shared set of operations available for each:

It also supports norms (2, n, 1/2, 1/n, ∞) and pseudoinverse, adjugate, and trace as functions.

How to enter matrices

You type elements into a grid, and the input accepts more than plain numbers:

• Decimals and fractions — 1/3, 3.14, -1.3(56) for repeating decimals, or 1.2e-4 for scientific notation.
• Mathematical expressions — 2/3+3*(10-4), (1+x)/y^2, 2^0.5, 2^(1/3), sin(phi), cos(3.142rad), or a_1.
• Matrix literals — {{1,3},{4,5}} written directly.
• Symbolic constants and variables — pi, e, i; k and n as integers; I or E for the identity matrix; X, Y as matrix symbols.

Navigation uses Enter, Space, the arrow keys, Backspace, and Delete to move between cells. You can copy and paste with Ctrl/Cmd + C and Ctrl/Cmd + V, and drag-and-drop matrices from the results or between the tool and a text editor.

Worked examples from the site

The page lists ready-made examples you can adapt:

• {{11,3},{7,11}}*{{8,0,1},{0,3,5}} — matrix multiplication
• determinant({{1,2,3},{4,5,6},{7,2,9}}) — determinant
• {{1,2},{3,4}}^-1 — inverse
• {{1,2,3},{4,5,6},{7,2,9}}^-1 — inverse of a 3×3

Output and display options

Results can be shown with a chosen number of fraction digits or significant digits, and the display-decimals setting lets you control precision. A clean button resets the input.

When to use it

Reach for matrixcalc.org when you want a fast check on a determinant, inverse, or rank, need to solve a small linear system, or want to see a decomposition like LU or SVD without setting up a full environment. For non-square matrices, leave the extra cells empty. If you need to verify a step-by-step solution, the site states it provides solution steps for systems of linear equations, which makes it more than a black-box answer generator for that task.

Matrix Calculator (matrixcalc.org) supports four matrix decompositions: LU decomposition, Cholesky decomposition, QR decomposition, and Singular Value Decomposition (SVD). Each is available as a button in the matrix operation panel, so you select the decomposition you want and apply it to the matrix you have entered. The right choice depends on what the matrix looks like and what you need the factors for — for example, Cholesky only applies to symmetric positive-definite matrices, while SVD works on any matrix.

The four decompositions and when to use them

The site lists these alongside other operations such as determinant, inverse, transpose, rank, row echelon form, diagonalization, exponentiation, and solving systems of linear equations with solution steps.

How to run a decomposition

1. Enter your matrix elements into the matrix input grid. Extra cells can be left empty to enter non-square matrices.
2. Select the decomposition you want — LU, Cholesky, QR, or SVD — from the operation buttons.
3. Read the result in the output area. Results can be dragged and dropped, including to or from a text editor.

Input accepts decimals (including periodic fractions like -1.3(56) and scientific notation like 1.2e-4), fractions such as 1/3, and mathematical expressions such as 2/3+3*(10-4) or 2^0.5. Matrix literals use the form {{1,3},{4,5}}.

Practical notes

• If Cholesky fails or is unavailable for your matrix, the matrix is probably not symmetric positive-definite; use LU or SVD instead.
• SVD is the safe general choice when the matrix is rectangular or you are unsure of its properties.
• The calculator also exposes related functions that pair with decompositions, including rank, inverse, pseudoinverse, determinant, transpose, trace, and adjugate, which is useful when you want to verify a factor or continue working with the result.

Matrix Calculator (matrixcalc.org) accepts more than plain numbers in each cell. You can type decimal fractions, full mathematical expressions, matrix literals, named functions, constants like pi and e, and units like rad and deg directly into the input fields. Type the value or expression into a matrix cell and click the operation button — the calculator parses the expression before computing. This works for both matrix A and matrix B, and for the expression-based input modes such as A*X=B.

What you can type into a cell

The calculator's own help text lists four categories of accepted input.

Numbers and fractions

Mathematical expressions

You can enter a whole expression instead of a single value, for example 2/3+3*(10-4) or (1+x)/y^2. Supported operators include +, -, *, /, \, !, ^, ^{*}, and comparison signs such as ≠, =, ⩾, ⩽, >, <. Separators , and ; are also recognized.

Matrix literals

A matrix can be written inline with curly braces: {{1,3},{4,5}}. Each inner brace pair is a row. This is useful in the expression input modes, for example {{1,2,3},{4,5,6},{7,2,9}}^(-1).

Functions, constants, and units

• Functions: sqrt, cbrt, exp, log, abs, conjugate, arg, min, max, gcd, rank, adjugate, inverse, determinant, transpose, pseudoinverse, trace, and the trigonometric/hyperbolic families (cos, sin, tan, cot, cosh, sinh, tanh, coth, and their arc/ar inverses), plus derivative, factor, and resultant.
• Constants: pi, e, i.
• Integers: k, n.
• Identity matrix: I or E.
• Matrix symbols: X, Y.
• Units: rad, deg — for example cos(3.142rad).

Step-by-step: entering an expression

1. Click into a cell of Matrix A (or Matrix B).
2. Type the expression, e.g. 2^0.5 or sin(phi).
3. Move between cells with Enter, Space, or the arrow keys; delete with Backspace or Delete.
4. Leave extra cells empty if you need a non-square matrix.
5. Click the operation button (Determinant, Inverse, Transpose, Rank, Multiply by, Row echelon form, Diagonal matrix, To the power of, LU decomposition, Cholesky decomposition, and so on).

Expected result: the calculator evaluates the expression first, then applies the operation. For example, entering {{1,2,3},{4,5,6},{7,2,9}}^(-1) returns the inverse of that 3×3 matrix.

Practical tips

• Powers and roots: use ^ for powers (2^0.5 for √2, 2^(1/3) for a cube root) or the sqrt/cbrt functions.
• Copy and paste: Ctrl/Cmd + C and Ctrl/Cmd + V work for matrices, and you can drag-and-drop matrices from the results or between the calculator and a text editor.
• Display precision: the interface lets you set the number of fraction digits and the number of significant digits for the output.
• Cleaning input: the ↶ Clean control clears the current input.

Common sticking points

• Repeating decimals need the parentheses form -1.3(56), not a plain decimal.
• e is overloaded: in 1.2e-4 it is scientific notation, while standalone e is Euler's constant.
• Units matter for trig: cos(3.142rad) and cos(3.142deg) give different results, so state the unit when it isn't radians by default.
• Non-square matrices: leave the unused cells empty rather than filling them with zeros.

Yes. Matrix Calculator at matrixcalc.org can solve systems of linear equations written in the matrix form A*X=B. You enter the coefficient matrix A and the constant matrix B, and the site returns the solution along with the solution steps. It also handles related equation forms such as Y+A=B. The tool works on non-square matrices too, as long as you leave the extra cells empty.

How the A*X=B solver works

A system of linear equations can be written compactly as A*X=B, where:

• A is the coefficient matrix (one row per equation, one column per variable)
• X is the column vector of unknowns you want to find
• B is the constant matrix (the right-hand side values)

The calculator solves for X. Because the site also computes the inverse matrix and other operations, it can approach the system through matrix methods rather than only substitution.

Steps to solve a system

1. Open matrixcalc.org.
2. Enter the coefficients into Matrix A. For example, a 3-equation, 3-variable system uses a 3×3 matrix.
3. Enter the constants into Matrix B as a column.
4. Select the A*X=B option (the solver mode shown in the interface).
5. Run the calculation and read the solution, which is displayed together with the solution steps.

Example input format: the site accepts matrix literals such as {{1,2,3},{4,5,6},{7,2,9}}, so you can type a matrix directly instead of filling cells one by one.

What you can expect as output

• The solution vector X for the system.
• Solution steps, so you can follow how the result was reached.
• Support for multiple equations, since the matrices can be larger than 2×2.

Related equation forms

The interface also lists Y+A=B alongside A*X=B. This lets you solve matrix equations where the unknown matrix appears in an addition relationship, not only in a product.

Practical notes

• You can enter decimal fractions or mathematical expressions (for example 1/3, 2^0.5, sin(phi)), which is useful when coefficients are not whole numbers.
• Non-square matrices are allowed — leave extra cells empty.
• Navigation and editing use standard keys: Enter, Space, arrow keys, Backspace, and Delete; copy and paste with Ctrl/Cmd + C and Ctrl/Cmd + V.
• Results can be dragged and dropped from the results area, or to and from a text editor.

If your goal is simply to get the unknown values for a linear system, entering A and B and using the A*X=B solver is the direct path. If you also want to inspect the underlying structure, the same site offers determinant, inverse, rank, and decomposition tools that complement the solve.