## Abstract Algebra – Show that the set v of all vectors (defined as directed line segments) forms an infinite Abelian group with vector addition as a composition

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## Vector Spaces – Displays the conclusion under Addition for $mathcal {Q}$: set of square shapes on $mathbb {R} ^ n$

In my script it says:

The sentence $$mathcal {Q}$$ of all square shapes on R
n
is a subspace of the vector space V of all functions
$$f: mathbb {R} ^ n → mathbb {R}.$$ (Remember that there is a one-to-one correspondence between quadratic forms and
symmetrical matrices.)

I was just curious how to show it?
Closing under addition, scalar multiplication and non-emptiness?

I think if anyone can show me the conclusion by either addition or scalar multiplication, I can figure out the rest, but I'm just trying to get started with it.

## Private key – Bitcoin kernel query, initialization vector

I'm checking the bitcoin core source code. I follow the code that states that a duplicate sha 256 of the public key is required to obtain the IV and to use the master key for the encryption key for the encrypted wallet.dat file. So I did the following:
1. Set the passphrase for my walltt.dat file.
2. Has taken a Double Sha 256 for the compressed public key
3. Enter the passkey as the encryption key
4. Places the encrypted private key as input data.

I'm not getting the already calculated private key in my dumpwallet file. Did I miss a parameter for the above calculation?

I've also retrieved IV and Key from Github's running compiled program. The values ​​do not match those calculated manually. Thanks for the help in advance.

## Differential Geometry – A question about the sequence of the holomorphic vector bundle

In Huybrechts "Complex Geometry" P93 he wrote: "A sequence of holomorphic vector bundles $$0 rightarrow E rightarrow F rightarrow G rightarrow 0$$ is exactly if and only if $$0 rightarrow G ^ * rightarrow F ^ * rightarrow E ^ * rightarrow 0$$ is exactly.

As we know, for everyone $$x in U_i cap U_j$$ the matrix of $${ psi ^ {& # 39;} _ {ij} }$$ has the form $$begin {bmatrix} psi_ {ij} & * \ 0 & phi_ {ij} end {bmatrix}$$ ,then $$E$$ is a holomorphic subset of $$F$$there is a canonical injection $$E subset F$$,

Conversely, if $$E$$ is a subbundum of $$F$$ We can find cocycles of this form and the cokernel $$F / E$$ is described by the cocycles $$phi_ {ij}$$,

S0, For $$F ^ *$$, the matrix of $$( { psi ^ {& # 39;} _ {ij} } ^ {- 1}) ^ {T}$$ has the form $$begin {bmatrix} ( { psi_ {ij} } ^ {- 1}) ^ {T} & 0 \ * ^ {& # 39;} & ( { phi_ {ij} } ^ {- 1}) ^ {T} end {bmatrix}$$ ,

I wonder why the claim is not "$$0 rightarrow E ^ * rightarrow F ^ * rightarrow G ^ * rightarrow 0$$ is exactly "?

It should be noted that a vector bundle morphism is uniquely determined by a collection of holomorphic maps
$$lbrace f_i: U_i longrightarrow mathcal {M} _ {m times n} ( mathbb {C}) rbrace_i$$ so that $$f_i = psi # {i j} f_j psi_ {ji}$$, At this point I can define $$f_i = left ( begin {array} {ccc} mathbb {I} _m \ O \ end {array} right).$$

I prefer a detailed explanation, thank you!

## c – vector comparison regardless of position

main () {

int vetoresIguais= 0;

int vetor(3) = {10,20,5};

int vetor1(3)= {20,50,15};

int i;

int j;

for(i = 0; i < 3; i++){

for(j = i; j < 3;j++){

if(vetor(i) == vetor1(i)){

vetoresIguais++;
}
}
}

printf("%d",vetoresIguais);


}

The result of this code is 0 because it only compares the vector at one position. If I set the value 20 to the first position of the first vector, it means that it has two equal values, how to solve, so that all values ​​are compared and how many are specified. The values ​​are repeated regardless of whether the position is the same or not?

(Feel free to work, never kk learned, I'm new here)

## Stable vector bundle and Hitchin card

To let $$E$$ Be a stable vector bundle over a curve $$X$$, $$K_X$$ the canonical bundle of $$X$$, $$W$$ the base of the Hitchin card.

Is the Hitchin card $$H: H ^ 0 (E otimes E ^ * otimes K_X) rightarrow W$$ surjective?
If not, is there an example?

## c ++ – Passing the pointer array to a vector with CudaMemcpyDeviceToHost ()

I want to use a vector in the kernel of the program, but I can not use a direct vector in the kernel. Therefore, I use thrust :: vector in the main program and pass it to the pointer array in the argument in the kernel, if I would like to pass the d_odata in a h_odata vector the received error that the runtime check fails # 3 – the variable & # 39; h_odata & # 39; is used without being initialized. I do not declare values ​​of h_odata because it is not important to initialize h_odata. What is the problem with the assignment and the program?

#include
#include
#include
#include
#include
#include
#include
#include
#include

__global__ void transpose(float *odata, float *idata, int width, int height)
{
__shared__ float block(BLOCK_DIM)(BLOCK_DIM+1);

// read the matrix tile into shared memory
// load one element per thread from device memory (idata) and store it
// in transposed order in block()()
unsigned int xIndex = blockIdx.x * BLOCK_DIM + threadIdx.x;
unsigned int yIndex = blockIdx.y * BLOCK_DIM + threadIdx.y;
if((xIndex < width) && (yIndex < height))
{
unsigned int index_in = yIndex * width + xIndex;
}

// synchronise to ensure all writes to block()() have completed

// write the transposed matrix tile to global memory (odata) in linear order
xIndex = blockIdx.y * BLOCK_DIM + threadIdx.x;
yIndex = blockIdx.x * BLOCK_DIM + threadIdx.y;
if((xIndex < height) && (yIndex < width))
{
unsigned int index_out = yIndex * height + xIndex;
}
}

void main( int argc, char** argv)
{

const unsigned int size_x = 242;
const unsigned int size_y = 200;

// size of memory required to store the matrix
const unsigned int mem_size = sizeof(float) * size_x * size_y;

vectorh_idata;
srand(15235911);
for( unsigned int i = 0; i < (size_x * size_y); ++i)
{
h_idata.push_back((float)i);
}

//copy host to device
thrust::device_vector idata(h_idata);
float* d_idata =  thrust::raw_pointer_cast(&idata(0));

float* d_odata;
cudaMalloc( (void**) &d_odata, mem_size);

// setup execution parameters
int gridSize_x = (int) ceil((float) size_x / BLOCK_DIM);
int gridSize_y = (int) ceil((float) size_y / BLOCK_DIM);
dim3 grid(gridSize_x, gridSize_y , 1);
dim3 threads(BLOCK_DIM, BLOCK_DIM, 1);

transpose<<< grid, threads >>>(d_odata, d_idata, size_x, size_y);

// copy results from device to host
vector*h_odata;
cudaMemcpy(&h_odata(0), d_odata, (size_x * size_y),
cudaMemcpyDeviceToHost) ;
for(int i=0 ; i< size_x * size_y ; i++){
printf("h_odata(%d) =%f" ,i , h_odata(i));
printf("n");}

// cleanup memory
cudaFree(d_idata);
cudaFree(d_odata);

}


I do not know how to convert the pointer array in a kernel to a vector because I want to use the vector in the Continue program.

vector*h_odata;
cudaMemcpy(&h_odata(0), d_odata, (size_x * size_y), cudaMemcpyDeviceToHost) ;


## Ag.algebraic geometry – Can a simple vector bundle be isomorphic to its rotation?

To let $$V$$ Let be a vector bundle over an algebraic curve $$C$$, Is it possible that $$V cong V otimes L$$ for a trunk group $$L$$? This is definitely possible, though $$V$$ is decomposable, for example if $$V cong mathcal {O} _C oplus L$$ With $$L ^ 2 cong mathcal {O} _C$$, I want to show that $$V cong V otimes L$$ implied $$L cong mathcal {O} _C$$ if $$V$$ Is simple.

## Graphics – inconsistent vector representation over contour representation

I'm trying to draw the gradient vector field over the contour plot of a function. While the demo function seems to work very well with the demo, which out How do I use vector diagrams and gradient vectors? (first diagram), I get a pretty confusing vector diagram with my own function (second diagram). My gut feeling is that the vector should be orthogonal to the contours, as in the first diagram.

Am I doing something wrong here? I tried to kill the kernel and start a new one to avoid any carry-over effects from my previous environment, but was not lucky.

## Physics – How do I move and rotate an object with vector math along with another?

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