Matrix workspace

Matrix calculator.

Step 2 · Shape

Matrix A

Rows Columns

Try integers, decimals, or fractions such as -3/4.

Step 3 · Solve

Choose an operation

Selected from your matrices Matrix A 2 × 2

Reduce a matrix to its simplest row-equivalent form.

Step 4 · Understand

Ready when you are

Places

Pick an operation and your result will land here.

Transformation playground

Matrix transformations.

Drag î or ĵ to reshape the matrix. Turn on Edit basis to begin.

Keyboard

Focus î or ĵ, then use arrow keys to nudge its endpoint.

SpeedSlowFast

IdentityTransformed

What to notice

The plane keeps its area

Both basis arrows move, carrying every grid point with them.

Area scale: 1
Orientation: kept

where î lands(1, 0)

where ĵ lands(0, 1)

Basis endpoints

Keyboard alternative

Type exact coordinates when dragging is not convenient.

î x y

ĵ x y

Why do columns matter?

The first column tells you where the horizontal basis vector lands; the second column does the same for the vertical basis vector.

Factorisation explorer

SVD explorer.

A = UΣVᵀ

SVD in three moves

SVD decomposes any real rectangular matrix A as A = UΣVᵀ. The orthogonal matrices Vᵀ and U act like rotations or reflections, while Σ stretches, shrinks, or collapses along perpendicular axes. So any linear transformation can be understood as a rotation or reflection, followed by a stretch or collapse, then another rotation or reflection.

Try it: this explorer visualises the 2×2 case. Choose a matrix, then press Play factors or select a stage. Use Factor progress to explore between stages, watching the solid grid and canonical basis move toward the faint final A-grid.

Move the canonical grid through Vᵀ, Σ, and U.The solid grid shows the current stage; the faint grid shows final A.

SpeedSlowFast

Factor progressU

Matrix calculator.

Matrix A

Choose an operation

Ready when you are

Matrix transformations.

Vector sketchbook.

Projection lab.

SVD explorer.

SVD in three moves

Give it a name

Matrix calculator.

Matrix A

Choose an operation

Ready when you are

Matrix transformations.

Vector sketchbook.

Your vectors

Projection lab.

Project b onto span(a)

SVD explorer.

SVD in three moves