Linear algebra

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

Matrices are best written with the button of the menu. However, they can also be written with the keyboard as a vector of multiple same-dimension vectors, 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.

Linear algebra
Makers
	Vector
	Matrix
	Determinant
Buttons for vectors
	Scalar product, dot product
	Vector product, cross product
	Norm
	Element of vector
Buttons about matrices
	Determinant
	Inverse
	Transpose
	Identity matrix
	Element of matrix
Commands
	Dimension of a vector
	Dimensions of a matrix; first files, then rows
	Rank of a matrix; max number of linearly independent rows or columns
	A matrix whose rows are a base of the kernel
	A matrix whose rows are a base of the image
	A list of eigenvalues, repeated as many times as their multiplicity
	A matrix whose rows are eigenvectors, ordered matching the eigenvalues result list
	The Jordan normal form of the matrix, if it exists. It gives the lower triangular form but not the upper.
	Angle between two vectors.

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,...

Matrix layout modifiers
	Insert column at left
	Insert column at right
	Remove column
	Insert row above
	Insert row below
	Remove row