Newbetuts

suppose $|a|<1$, show that $\frac{z-a}{1-\overline{a}z}$ is a mobius transformation that sends $B(0,1)$ to itself.

Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent

only an even dimensional real vector space can admit a complex structure

why preserving norm is equivalent to preserving inner product in rigid body transformation

Show that the Area of image = Area of object $\cdot |\det(T)|$? Where $T$ is a linear transformation from $R^2 \rightarrow R^2$

Basis for $\mathbb R$ over $\mathbb Q$

$T: \mathbb{C}_{2020}[x]\to \mathbb{C}_{2020}[x]$, $\sum_{i=0}^{2020}a_ix^i \mapsto \sum_{i=0}^{2020}a_i(x-1)^i$

Gradient of $\lVert A(X) - b\rVert^2$ with $A$ a linear operator

A real function which is additive but not homogenous

Show that $\big\{A(v_{i_1}\otimes \cdots\otimes v_{i_k})\in V^{\wedge k}:i_1<\cdots<i_k \big\} $ is linearly independent

The rank of a linear transformation/matrix

How do I determine whether or not an isomorphism $T:V\to W$ is a canonical isomorphism?

What is the interval of W(A)

If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$

Any linear subspace has measure zero

Active and passive transformations in Linear Algebra

If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$

New posts in linear-transformations

Definitions of "linearity" across branches of mathematics or levels of math education

Unitary matrix commute with function

When is $A^TBA$ invertible, where $B$ is an invertible, symmetric matrix?

suppose $|a|<1$, show that $\frac{z-a}{1-\overline{a}z}$ is a mobius transformation that sends $B(0,1)$ to itself.

Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent

only an even dimensional real vector space can admit a complex structure

why preserving norm is equivalent to preserving inner product in rigid body transformation

Show that the Area of image = Area of object $\cdot |\det(T)|$? Where $T$ is a linear transformation from $R^2 \rightarrow R^2$

Basis for $\mathbb R$ over $\mathbb Q$

$T: \mathbb{C}_{2020}[x]\to \mathbb{C}_{2020}[x]$, $\sum_{i=0}^{2020}a_ix^i \mapsto \sum_{i=0}^{2020}a_i(x-1)^i$

Gradient of $\lVert A(X) - b\rVert^2$ with $A$ a linear operator

A real function which is additive but not homogenous

Show that $\big\{A(v_{i_1}\otimes \cdots\otimes v_{i_k})\in V^{\wedge k}:i_1<\cdots<i_k \big\} $ is linearly independent

The rank of a linear transformation/matrix

How do I determine whether or not an isomorphism $T:V\to W$ is a canonical isomorphism?

What is the interval of W(A)

If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$

Any linear subspace has measure zero

Active and passive transformations in Linear Algebra

If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$