Figuring out kyle numbers for matrices/

  • Thread starter Thread starter Witt27
  • Start date Start date
  • Tags Tags
    Matrices Numbers
Click For Summary
SUMMARY

The discussion focuses on understanding Kyle numbers in relation to matrices, specifically the example where the numbers 1 and 2 are derived from the linear combination of matrix columns resulting in a zero vector. The key concept involves finding the Kernel of the matrix, which is the subspace that transforms to zero under a linear transformation. The user highlights confusion regarding the explanation that adding the first column to two times the second column yields zero, clarifying that the correct operation is two times the first column added to the second column.

PREREQUISITES
  • Understanding of linear transformations
  • Familiarity with matrix operations
  • Knowledge of Kernel in linear algebra
  • Ability to perform row-reduction on matrices
NEXT STEPS
  • Study the concept of Kernel in linear algebra
  • Learn about linear combinations of vectors
  • Practice row-reduction techniques on matrices
  • Explore examples of linear transformations and their properties
USEFUL FOR

Students of linear algebra, educators teaching matrix theory, and anyone seeking to deepen their understanding of linear transformations and Kernel concepts.

Witt27
Messages
1
Reaction score
0

Homework Statement


http://www.math.harvard.edu/archive/21b_spring_09/faq.html
I'm having trouble understanding this explanation, particularly this part. "The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. "
Sorry for this basic question but I was wondering if someone can explain this particular part.

Homework Equations


NA

The Attempt at a Solution


NA
 
Physics news on Phys.org
In principle, you have to find the Kernel of the matrix, that is the subspace the elements of which become zero by applying the linear transformation. In the example, the elements are multiples of the vector [1,2]T. You can find the elements of the Kernel by row-reduction of the matrix, but I do not understand the sentence you cited "The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. "
Two times the first column added to the second one gives zero. So 1,2 are the numbers in the linear combination of the columns that produces null vector.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 17 ·
Replies
17
Views
9K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
8K
  • · Replies 7 ·
Replies
7
Views
3K