Leitner

Learn linear algebra by moving the vectors yourself

Linear algebra is usually taught as arithmetic on grids of numbers, and then one day somebody tells you the matrix was a transformation all along. The order is backwards: the geometry is the idea and the arithmetic is the bookkeeping. So the block below hands you the two basis vectors and lets you drag them, because a matrix is nothing but where those two vectors land.

Drag î or ĵ. The matrix and the determinant follow — collapse them onto a line and the determinant goes to zero.

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.

Start a linear algebra planThe first lesson of every plan is free

What people come here to do

You describe the goal in your own words and it asks questions back until the plan is one you would actually follow. These are the shapes that goal usually takes.

  • 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

Not a fixed syllabus — the plan is built around your goal and cuts what does not serve it. These are the topics it draws from, and whatever you get wrong comes back until it stops coming back.

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

The mechanics are the same whatever the subject — a slider is a slider whether it is moving a coefficient or a rate of return. What changes is what it is a slider for.

Or see how it works and what it costs.