New posts in Linear Transformations

Proving a linear transformation is unique

Geometrically explained, why do Linear Transformations Take a circle to an ellipse

Finding the characteristic polynomial of the $T: \mathcal{M}_{n} (\mathbb{R}) \to \mathcal{M}_{n} (\mathbb{R})$ given by $T(M)=M^{\text{tr}}$

Is it true that the eigenvalues of $A + B$ are the sum of some eigenvalue of $A$ and some eigenvalue of $B$?

Why linear maps act like matrix multiplication?

Does the action of a linear map on $k$-dimensional subspaces determine it up to scaling?

Proper way to find change-of-basis matrix

Show that matrix of $T$ has at least dim range $T$ nonzero entries.

Is $0$ the only vector in the kernel of every bounded linear functional?

Let $T\colon \mathbb{R}^2 \to \mathbb{R}^2$ be linear transformation. Show that there are $a,b\in \mathbb{R}$ such that $T^2+aT+bI=0$.