Linear algebra – Graphical representation of differential vector equations

My book of linear algebra deals with differential vector equations, and they give the example of function $ x (t) = (-3/70) begin {bmatrix} -5 \ 2 end {bmatrix} e ^ {6t} + (188/70) begin {bmatrix} 1 \ 1 end { bmatrix} e ^ {- t} $. They then graph the function as follows: graphic
The thing is that when I plug in numbers for $ t $and graph by hand, I only have one line – not all of these lines as they show on this graph and similar graphs. So I am confused about what they are doing here. Can anyone explain to me how to correctly represent these equations? Thank you.

photoshop – How to create a flat vector photo / photo from an original photo?

This type of color reduction has become popular with the "Obama Hope" poster, and the search for plugins under that name has produced results. Another method is to "posterize" the image to reduce the number of colors (and hope for the best) or to sample a few dominant colors in a palette, then convert the image to use the palette.

OTOH, you can't take a random photo and expect good results. This will only work with specific images, with good contrast and few colors, and probably a lot of "manual help".

c ++ – How to round the elements of a vector?

– replace each element with its whole
for (2.72,4.34,9.82,,2.45)
cost 2 4 9 1 4 2.

i tried that

using namespace std;
int main()
    int n;
    double v(100),i;

but I get this error:

|10|error: invalid types 'double (100)(double)' for array subscript|
|13|error: invalid types 'double (100)(double)' for array subscript|
|16|error: invalid types 'double (100)(double)' for array subscript|

Linear algebra – Given that $ W_ {1} cup W_ {2} $ is a vector space, prove that one of the spaces $ W_ {i} $ is contained in the other.

Let $ W_ {1} $ and $ W_ {2} $ to be subspaces of a vector space $ V $ so that the theoretical union of the whole $ W_ {1} $ and $ W_ {2} $ is also a subspace. Prove that one of the spaces $ W_ {i} $ is contained in the other.


From a geometric point of view, it is intuitive to interpret it when we consider different lines passing through the origin in $ textbf {R} ^ {2} $ or different planes going through the origin when you consider $ textbf {R} ^ {3} $: There is no way to maintain the proposed result unless one line (or a plane) is contained in the other. However, I am unable to convert such a geometric interpretation into proof.

Any help is appreciated.

how to convert a vector contains vectors every 8 bit vector i want to change every 8 bit to decimal

how to convert a vector contains vectors each 8 bit vector i want to change each 8 bit to decimal then i want to plot the image with img = Image [vector, "Byte"]

vector spaces – Identities for subspaces and line maps

Wikipedia has a nice list of identities for how intersections, unions, and complements interact with images and pre-images of whole functions.

But if $ f: V to W $ is a linear map, many identities for the overall functions can be refined. For example, if $ A subset V $, then $ f ^ {- 1} (f (A)) = A + ker f $. There are also identities that involve sums, for example $ f (A + B) = f (A) + f (B) $.

Can anyone tell me a reference containing a list of identities for subspaces and line maps?

adjustment – Mathematica is slow to estimate the parameters of the vector autoregressive model

I have been trying to get VAR model parameters using EstimatedProcess and FindProcessParameters. It seems like it takes a long time as soon as I have more than 6 or 7 time series and an offset> 2.

The data I use is the z-rated daily newspaper of the financial time series, with around 1000 data points.

It works fine up to 8 sets with shift 2 and only up to 6 sets with shift 3 (taking 15 minutes for the last one). Anything above that doesn't seem to be working or is really very slow. EstimatedProcess has been running for 3 hours now for a process p = 3 VAR with 7 time series.

I have also tried this on data that I simulated using ARProcess and the problem is the same, it is time consuming and above a number of series and latency, it doesn't return results (unless I haven't waited long enough).

Any help would be greatly appreciated.

co.combinatorics – Build a vector composed of non-financial inputs

Consider building a vector $ v = {a_1, a_2, ldots, a_n } $ composed of non-negative integers such as $ a_1 = $ 1 and if $ a_j $are non-zero, then $ a_j equiv a_ {n-j + 1} + j ( bmod m) forall j neq1 $, or $ m $ be the number of non-zero entries; with the additional constraint that everything not zero $ a_i $are distinct.

Is it still possible to build such a vector? I think it should be possible if $ m $ is odd. For example, $ {1,4,2,5,3 } $ or $ {1,4,2,0,0,5,3 } $ are such vectors. It is easy to build if the first entries (in $ lfloor frac {n} {2} rfloor $ ) of the vector are consecutive. But, in other cases, the way to proceed with the construction is unclear. Clues? Thanks in advance.

vector graphics – Tecplot: I can't see the Latin Modern font

I installed in my Windows 10 system the Latin Modern Roman font (the whole family). I cannot work with these fonts in Tecplot. They do not appear in any Tecplot font menu. I want to use them in all the fonts on my plot (label and axis numbers, title, annotation, etc.).
I want to use this font (and no other) because it is the default Latex font. I don't want to use the Tecplot Latex app because I want to use this font even in the axis numbers.
How to deal with this situation?

Some font features are: OpenType layout, PostScript outlines
Version: Tecplot 360 2013R1

Standardized vector and set. Can anyone help me prove it?

If we leave { $ widehat x_i $ } be the normalized dataset of {$ x_i $} which has N elements, proves the vector <$ frac {( widehat x_1)} {( sqrt n)} $, $ frac {( widehat x_2)} {( sqrt n)} $, …… $ frac {( widehat x_n)} {( sqrt n)} $> has a unit length.