Nullity and rank of the linear transformation $T[f(t)] = \int_a^b f(t) \sin (x-t) dt ~\forall~x \in [a,b]$
87254
The computation of nullity and rank of a linear transformation.
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
37953
Primary Decomposition of $\mathbb{R^n}$ under T
59804
Show that the plane $\{su+tv|s,t \in\Bbb R\}$ in $\Bbb R^3$ is equal to the null space of some element of $(\Bbb R^3)^{*}$.
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
23580
Range of A and null space of the transpose of A
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
72654
If $(a_n)$ is a null sequence and $(b_n)$ is bounded, then $(a_nb_n)$ is a null sequence
16049
Fourier transform of $\int_{-\infty}^{t}f(t)\, dt$
78307
Under what conditions is $AA^T$ invertible?
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
20021
Convolution integral $\int_0^t \cos(t-s)\sin(s)\ ds$