MHB The Significance of Row Space in a Matrix

matqkks
Messages
280
Reaction score
5
Why is row space of a matrix important?
 
Physics news on Phys.org
matqkks said:
Why is row space of a matrix important?

Hi matqkks, :)

Can you elaborate what do you mean by "important"? Do you want to connect this concept with some practical applications?

Kind Regards,
Sudharaka.
 
We know that the linear system Ax=b has a solution iff b is in the column space of matrix A. So column space needs no other motivation for students. THe only time I tend to use row space is to define rank of matrix.
Really what I am asking is 'why should students want to learn about row space?'
 
matqkks said:
We know that the linear system Ax=b has a solution iff b is in the column space of matrix A. So column space needs no other motivation for students. THe only time I tend to use row space is to define rank of matrix.
Really what I am asking is 'why should students want to learn about row space?'

Well in that sense, the row space is important in establishing the rank of a matrix, which in turn has useful applications(See this and http://www.mathhelpboards.com/f14/rank-1618/#post7582).

Kind Regards,
Sudharaka.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
View full post »

Similar threads

I Row space, Column space, Null space & Left null space
  • · Replies 8 ·
Replies
8
Views
3K
I In 4x4 matrix when does row swapping not affect eigenvaluess?
  • · Replies 6 ·
Replies
6
Views
3K
B How to multiply matrix with row vector?
  • · Replies 4 ·
Replies
4
Views
3K
B Finding Bases for Row and Column Spaces
  • · Replies 1 ·
Replies
1
Views
2K
I Cycles from patterns in a permutation matrix
  • · Replies 3 ·
Replies
3
Views
2K
I Vector subspace and basis vectors in the context of data science
  • · Replies 6 ·
Replies
6
Views
3K
I Are the columns space and row space same for idempotent matrix?
  • · Replies 6 ·
Replies
6
Views
3K
I Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
I Matrix diagonalization algorithm
  • · Replies 5 ·
Replies
5
Views
2K
I Problem with notation of matrix elements
  • · Replies 3 ·
Replies
3
Views
2K