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Learn linear algebra by moving the vectors yourself

Start a linear algebra plan, first lesson free
Linear algebra · transformsDET 1.00
matrix[1.00 0.00 ; 0.00 1.00]det1.00

The square spans 1.00 units of area. That is the determinant, and it is the factor every area in the plane is multiplied by. Drag a vector until the square is twice the size and the whole plane doubles with it.

Drag î or ĵ and the matrix and determinant follow; squash them onto one line and the determinant goes to zero.

Linear algebra usually arrives as arithmetic on grids of numbers, and later someone mentions the matrix was a transformation all along. That order is backwards. The geometry is the idea and the arithmetic is bookkeeping. So the block below gives you the two basis vectors to drag, because a matrix is just where those two vectors land.

What people come here to do

You describe the goal in your own words and the plan asks questions back until it is one you would follow. Goals usually look like these.

  • “Pass a linear algebra paper without memorising row reduction”
  • “Understand what eigenvectors are actually for”
  • “Get the linear algebra a machine learning course assumes”
  • “Finally see why a determinant of zero means no inverse”

What a linear algebra plan covers

There is no fixed syllabus. The plan is built around your goal and drops what it does not need. These are the topics it draws from.

  • Vectors, spans and linear combinations
  • Matrices as transformations of space
  • Determinants, area and orientation
  • Inverses, rank and what singular means
  • Eigenvalues and eigenvectors
  • Least squares and projection

Other subjects

Each one has its own lesson block to try.

See how it works and what it costs.