A linear operator in Rn x n is a function that maps a vector in Rn to another vector in Rn, using a matrix multiplication operation.
A linear operator is a function, while a matrix is a representation of that function. A linear operator can be represented by different matrices depending on the chosen basis, while a matrix is a fixed representation.
The inverse of a linear operator in Rn x n can be calculated using the inverse of its corresponding matrix. If the matrix is invertible, then the inverse exists and is also a linear operator.
The eigenvalues and eigenvectors of a linear operator in Rn x n represent the scaling factor and direction, respectively, of the vectors that do not change direction when the linear operator is applied.
Linear operators in Rn x n have a wide range of applications in various fields such as physics, engineering, and computer science. They are used for solving systems of linear equations, transformations in 3D graphics, signal processing, and quantum mechanics, among others.