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Linear Algebra

Linear algebra is the detailed study of vector spaces. With applications in such disparate fields as sociology, economics, computer programming, chemistry, and physics, including its essential role in mathematically describing quantum mechanics and the theory of relativity, linear algebra has become one of the most essential mathematical disciplines for the modern world. Please direct all questions regarding matrices, determinants, eigenvalues, eigenvectors, and linear transformations into this category.

2,176 Questions

How do you do dot product of the vectors at any dimension?

You do the dot product of the vectors by multiplying their corresponding coordinates and adding them up altogether. For instance:

<1,2,3> ∙ <-3,4,-1>

= 1(-3) + 2(4) + 3(-1)

= -3 + 8 - 3

= 2

How do you write an equation that is purpendicular to another?

Make the slope a negative reciprocal. That means that you change the sign ( a positive number becomes negative or a negative number becomes a positive ). You also flip the slope as though it were a fraction (4/5 becomes 5/4. And 2/1 becomes 1/2).

So if the slope was 3x it would now be -1/3x.

Is y2x2 a function?

I am almost sure it is not.

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question.

Can you write the equation out?

Yes, you can write an equation out in words. This is often done to make clear what the equation in numerals is.

Name any uses for dot product or cross product in video games?

The cross product is used to find surface normals of triangles (the building blocks of objects in 3D games). Those surface normals can then be used in dot product tests with the camera to test if the normal is facing the camera or not. If the dot product angle is positive then the normal is facing the same direction as the camera, so the triangle does not need to be drawn (because it cannot be seen). If the angle is negative, then the two vectors are pointing at each other and the triangle may need to be rendered. These methods not only apply to camera viewing, but also to lighting and physics calculations as well.

What type of symmetry is best suited for movement?

People are bilateral, two sided. As we move we push one side against the other. Imagine the ice skater pushing to the right and then the left.

Fish are another example. The fish push back and forth to move through the water.

How you write 45987 in a word?

forty-five thousand, nine hundred and eighty-seven

What is algebraist in math?

An algebraist is someone who studies algebra. Usually, "algebra" in this context means "abstract algebra." Thus an algebraist studies groups, rings, fields, etc. See http://en.wikipedia.org/wiki/Abstract_algebra

A geometer studies geometry. A topologist studies topology. An analyst studies analysis (think calculus, but for mathematicians.)

Pgm to check given matrix is diagonal or not?

#include <stdio.h> #include <conio.h> void main() { int a[3][3],i,j,flg=0,flg2=0; clrscr(); printf("\n\t Enter 3*3 Matrix : "); for(i=0;i<3;i++) { for(j=0;j<3;j++) { scanf("%d",&a[i][j]); } } for(i=0;i<3;i++) { for(j=0;j<3;j++) { if(a[i]<a[j] && a[i][j]==0) { flg=flg+1; } if(a[i]>a[j] && a[i][j]==0) { flg2=flg2+1; } } } if(flg==3 && flg2==3) printf("\n\n Diagonal matrix !"); else printf("\n\n Not Diagonal matrix !"); getch(); }

What is the different kinds of linear system according to slope?

The question makes little general sense because the concept of slopes is appropriate when dealing with equations in only two variables.

Assuming, therefore, that there are only two variables, then either the slopes are the same or they are different,


If the slopes are the same and the intercepts are the same: there are infinitely many solutions

If the slopes are the same and the intercepts are different: there are no solutions

If the slopes are different: there is a unique solution.



What is the reason to use a math?

  1. While shopping to add the total cost or calculate the discount.
  2. In Computer Programming.
  3. In Rocket Science.
  4. To calculate the distance between banks of a river before crossing it!
  5. To calculate the time of journey from one place to another.
  6. ...And anything you can think of!