Matrix geometric interpretation
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What is the geometric interpretation of a matrix with only one element? If it means One dimension then how to identify the dimension viz X,YorZ?
linear-algebra
asked Aug 19 at 6:11
Mahesh
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favorite
What is the geometric interpretation of a matrix with only one element? If it means One dimension then how to identify the dimension viz X,YorZ?
linear-algebra
asked Aug 19 at 6:11
Mahesh
11
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is the geometric interpretation of a matrix with only one element? If it means One dimension then how to identify the dimension viz X,YorZ?
linear-algebra
asked Aug 19 at 6:11
Mahesh
11
What is the geometric interpretation of a matrix with only one element? If it means One dimension then how to identify the dimension viz X,YorZ?
linear-algebra
asked Aug 19 at 6:11
Mahesh
11
asked Aug 19 at 6:11
Mahesh
11
asked Aug 19 at 6:11
Mahesh
11
asked Aug 19 at 6:11
Mahesh
11
11
add a comment |Â
add a comment |Â
2 Answers
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oldest
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0
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This is not an answer just a share of thought or discussion.
In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
add a comment |Â
up vote
0
down vote
A $1 times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".
If you represent a $2 times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.
answered Aug 19 at 7:26
Omnomnomnom
122k784170
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
This is not an answer just a share of thought or discussion.
In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
add a comment |Â
up vote
0
down vote
This is not an answer just a share of thought or discussion.
In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
add a comment |Â
up vote
0
down vote
up vote
0
down vote
This is not an answer just a share of thought or discussion.
In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
This is not an answer just a share of thought or discussion.
In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
answered Aug 19 at 6:24
Sujit Bhattacharyya
457116
457116
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
add a comment |Â
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
Thanks for replying...My Query is if we can represent the 2*2 matrix using column vectors. How are we going to represent 1*1 matrix geometrically?
– Mahesh
Aug 19 at 7:02
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
did you mean this: Let, $A_1times 1=(a)_1times 1$ then $A_1times 1=abullet (1)_1times 1$, $a$ is a scalar quantity.
– Sujit Bhattacharyya
Aug 20 at 9:59
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar.
– Mahesh
Aug 21 at 11:08
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
check this out : quora.com/Is-a-1-x-1-matrix-a-scalar
– Sujit Bhattacharyya
Aug 22 at 3:58
add a comment |Â
up vote
0
down vote
A $1 times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".
If you represent a $2 times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.
answered Aug 19 at 7:26
Omnomnomnom
122k784170
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
add a comment |Â
up vote
0
down vote
A $1 times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".
If you represent a $2 times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.
answered Aug 19 at 7:26
Omnomnomnom
122k784170
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
add a comment |Â
up vote
0
down vote
up vote
0
down vote
A $1 times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".
If you represent a $2 times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.
answered Aug 19 at 7:26
Omnomnomnom
122k784170
A $1 times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".
If you represent a $2 times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.
answered Aug 19 at 7:26
Omnomnomnom
122k784170
answered Aug 19 at 7:26
Omnomnomnom
122k784170
answered Aug 19 at 7:26
Omnomnomnom
122k784170
answered Aug 19 at 7:26
Omnomnomnom
122k784170
122k784170
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
add a comment |Â
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
My answer here regarding $1 times 1$ matrices also comes to mind.
– Omnomnomnom
Aug 19 at 7:29
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
Thanks for replying...So the Vectors concerned are the Unit vectors .
– Mahesh
Aug 19 at 7:34
add a comment |Â
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