Linear algebra

Find the operations on vectors and matrices here. Vectors, which use brackets, are written horizontally. You can write them with the men's buttons or directly with the keyboard.

Matrices are best written using the menu button. However, they can also be written with the keyboard as a vector of multiple vectors of the same dimension, as in many programming languages. Once a matrix is created, you can still modify its layout. You can, for example, insert or remove columns and rows. There are buttons for that in the menu. Usually, they're disabled, but they become enabled when the cursor enters a matrix.

Vectors are automatically seen as matrices by some commands. You needn't be concerned about the conversion. The usual operations are aware of vectors and matrices. For example, the common product symbol means different things when used between a scalar and a vector, two vectors, a vector and a matrix, or two matrices.

For the kernel(), image() and eigenvectors() commands, the result is a matrix whose columns are the vectors that form a base. Note that, because there are always many bases, there are many other correct results. You can get a particular vector from the result R using R^T₁, R^T₂, R^T₃,...

Examples