Matrix Row & Column Operations
Let $A$ be an $m times n$ matrix. Then by applying a sequence of row and column operations, $A$ can be reduced to the following form
begin{pmatrix}
I_r & O_{r times n - r}\
O_{m - r times r} &O_{m - r times n - r}
end{pmatrix}
Above is indeed a big $m times n$ matrix with entries a11, a12, a21, a22.
$O$ is a Zero matrix.
I don't get how we are getting matrix within a matrix by transformations?
linear-algebra matrix-calculus matrix-analysis
edited Jan 4 at 15:37
amWhy
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
add a comment |
Let $A$ be an $m times n$ matrix. Then by applying a sequence of row and column operations, $A$ can be reduced to the following form
begin{pmatrix}
I_r & O_{r times n - r}\
O_{m - r times r} &O_{m - r times n - r}
end{pmatrix}
Above is indeed a big $m times n$ matrix with entries a11, a12, a21, a22.
$O$ is a Zero matrix.
I don't get how we are getting matrix within a matrix by transformations?
linear-algebra matrix-calculus matrix-analysis
edited Jan 4 at 15:37
amWhy
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
1
The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49
add a comment |
Let $A$ be an $m times n$ matrix. Then by applying a sequence of row and column operations, $A$ can be reduced to the following form
begin{pmatrix}
I_r & O_{r times n - r}\
O_{m - r times r} &O_{m - r times n - r}
end{pmatrix}
Above is indeed a big $m times n$ matrix with entries a11, a12, a21, a22.
$O$ is a Zero matrix.
I don't get how we are getting matrix within a matrix by transformations?
linear-algebra matrix-calculus matrix-analysis
edited Jan 4 at 15:37
amWhy
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
Let $A$ be an $m times n$ matrix. Then by applying a sequence of row and column operations, $A$ can be reduced to the following form
begin{pmatrix}
I_r & O_{r times n - r}\
O_{m - r times r} &O_{m - r times n - r}
end{pmatrix}
Above is indeed a big $m times n$ matrix with entries a11, a12, a21, a22.
$O$ is a Zero matrix.
I don't get how we are getting matrix within a matrix by transformations?
linear-algebra matrix-calculus matrix-analysis
linear-algebra matrix-calculus matrix-analysis
edited Jan 4 at 15:37
amWhy
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
edited Jan 4 at 15:37
amWhy
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
edited Jan 4 at 15:37
amWhy
192k28225439
edited Jan 4 at 15:37
amWhy
192k28225439
edited Jan 4 at 15:37
amWhy
192k28225439
192k28225439
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
asked Jan 4 at 14:39
Onkar SinghOnkar Singh
62
62
1
The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49
add a comment |
1
The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49
1
1
The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49
add a comment |
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The "matrix in a matrix" is just notation for looking at different submatricse. It helps make it easier to talk about the structure of certain parts of a matrix. The wikipedia page on block matrices may be of interest.
– tch
Jan 4 at 14:46
Someone also tell me how can I form matrix itself in the question by Mobile App?
– Onkar Singh
Jan 4 at 14:47
@tch The wiki page at least gave me the idea, thanks a lot.
– Onkar Singh
Jan 4 at 14:49