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A scalar value that is a function of the entries of a square matrix and encodes certain properties of the linear transformation.

The set of all linear combinations of the row vectors of a matrix.

A matrix that, when multiplied by the original matrix, yields the identity matrix.

A set of vectors in which no vector can be written as a linear combination of the others.

A subset of a vector space that is itself a vector space under the same operations.

The dimension of the vector space spanned by the columns (or rows) of the matrix.

A non-zero vector that changes at most by a scalar factor when that linear transformation is applied.

A collection of vectors which can be added together and multiplied by scalars while satisfying certain axioms.

The set of all possible linear combinations of a given set of vectors.

A rectangular array of numbers, symbols, or expressions arranged in rows and columns that represents a linear transformation.

The set of all vectors that, when multiplied by the matrix, result in the zero vector.

The set of all linear combinations of the column vectors of a matrix.

A set of vectors in a given vector space V that is linearly independent and spans V.

A scalar associated with a linear system of equations that, when multiplied by an Eigenvector of the system, yields that Eigenvector scaled by the scalar.