finding space basis in matlab

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ne ne
ne ne 2018-12-27
编辑： John D'Errico 2020-12-4
hello!i am new to matlab and i really would appreciate your help. I need to make a funtion into which i can put an mxn table. This function will find the basis of the space R(A) and the basis of space R(A').
  2 个评论
madhan ravi
madhan ravi 2018-12-27
what's R? what's A? what's your desire output ? Give an example ?
ne ne
ne ne 2018-12-27
A is an mxn table. I have to make this function in order for it to be used in any table given.
R is a space that contains all of the vectors of A.
for example I have to put the table A=[3 -1 7 3 9; -2 2 -2 7 5; -5 9 3 3 4; -2 6 6 3 7 ]

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回答（1 个）

John D'Errico
John D'Errico 2018-12-27
编辑：John D'Errico 2018-12-27
A=[3 -1 7 3 9; -2 2 -2 7 5; -5 9 3 3 4; -2 6 6 3 7 ]
A is a matrix, not a table. This is a table:
T = table(A)
T =
4×1 table
A
__________________________
3 -1 7 3 9
-2 2 -2 7 5
-5 9 3 3 4
-2 6 6 3 7
If you have actually stored A as a table, then you can extract the data from it using table2array. Regardless, if all you want to do is form the row and column basis representations for a matrix A, this is easy enough. Just use orth, twice.
Note that A was 4x5, but with a rank of 3, as we learn here:
rank(A)
ans =
3
So each basis system will have three basis vectors. The row space of A is spanned by three row vectors:
orth(A.').'
ans =
0.16491 -0.45832 -0.42192 -0.3853 -0.66051
0.55328 -0.63554 0.38877 -0.062596 0.3673
0.0042955 -0.31674 -0.62059 0.68313 0.21877
And the column space of A is spanned by three column vectors.
orth(A)
ans =
-0.48382 0.79099 0.0005431
-0.34036 -0.17083 0.92116
-0.53232 -0.58716 -0.25742
-0.60556 -0.019817 -0.2919
  1 个评论
John D'Errico
John D'Errico 2020-12-4
编辑：John D'Errico 2020-12-4
@SAJJA BALA KARTHIKEYA asked a question (which I have moved into this comment):
"how to find row space of a matrix?"
First, this is not an answer to the question. It is just another question, saying that you did not understand my answer.
But then I would be forced to ask what did I mean when I explicitly stated the solution in my answer:
The row space of A is spanned by the row vectors:
orth(A.').'
As such, your question (asked as an answer) already had an answer.

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