If we apply A as a linear transformation to the standard base, aka the identity matrix, we get A itself. However, we could consider this transformation as it transforms the basis vectors to all …

This is because of linearity.) If you manage to obtain the identity matrix on the left, then you know the images of the vectors from the standard basis, which is sufficient to obtain the matrix of …

Oct 31, 2015 · The third property you mentioned basically says that linear transformation are the same as matrix transformations. So every linear transformation has a matrix corresponding to …

May 28, 2014 · Could you give me an example of non linear transformation matrix? What is the difference between linear and non linear transformation matrix?

We have theorems and techniques for finite dimensional vector spaces that associate (a linear transformation + a basis) with a matrix. By mapping elements (via the choice of basis) to …

Jan 5, 2021 · The definition of one-to-one was pretty straight forward. If the vectors are lin.indep the transformation would be one-to-one. But could it also be onto? The definition of onto was a …

A reflection is a linear transformation on the plane with eigenvalues $\pm 1$ and orthogonal eigenvectors. The line spanned by the eigenvector with eigenvalue $1$ is called the reflection …

Mar 11, 2020 · I'm not sure if this is just a pedantic issue of notation, or a conceptual misunderstanding on my part. I am studying from Sergei Treil's Linear Algebra Done Wrong. …

Oct 7, 2023 · We usually use the action of the map on the basis elements of the domain to get the matrix representing the linear map. In this problem, we must solve two systems of equations …

30 I just came back from an intense linear algebra lecture which showed that linear transformations could be represented by transformation matrices; with more generalization, it …