If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
62280
If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective.
24107
Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
147450
Prove that every bilinear map can be written as a sum of bilinear symmetric map and a bilinear anti-symmetric map.
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
10001
Prove that the only eigenvalue of a nilpotent operator is 0?
82448
Why is $f(x) = x\phi(x)$ one-to-one?
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
10307
Show the inverse of a bijective function is bijective
158534
Proof that any linear system cannot have exactly 2 solutions.
140212
Prove that there exists a unique linear map that extends the map from a basis
63845
Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
100107
How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?