Correct notation for writing array reshape
Suppose I am coding in python.
Then one can do e.g. something like this:
import numpy as np
A = np.random.rand((6,6))
# Lets reshape it
A_new = A.reshape(-1,3)
So it went from 2D array (matrix) to a 2D array with six 12 rows and three columns.
How would one write the re-shape operation formally in mathematical notation? Transpose is obviously easy, but is there a parallel for reshapes?
$$mathbf{A} in mathbb{R}^{6times6} rightarrow mathbf{A} in mathbb{R}^{12 times 3}$$
Thx
matrices notation vectors matrix-equations
asked Nov 26 at 15:13
Astrid
283114
add a comment |
Suppose I am coding in python.
Then one can do e.g. something like this:
import numpy as np
A = np.random.rand((6,6))
# Lets reshape it
A_new = A.reshape(-1,3)
So it went from 2D array (matrix) to a 2D array with six 12 rows and three columns.
How would one write the re-shape operation formally in mathematical notation? Transpose is obviously easy, but is there a parallel for reshapes?
$$mathbf{A} in mathbb{R}^{6times6} rightarrow mathbf{A} in mathbb{R}^{12 times 3}$$
Thx
matrices notation vectors matrix-equations
asked Nov 26 at 15:13
Astrid
283114
add a comment |
Suppose I am coding in python.
Then one can do e.g. something like this:
import numpy as np
A = np.random.rand((6,6))
# Lets reshape it
A_new = A.reshape(-1,3)
So it went from 2D array (matrix) to a 2D array with six 12 rows and three columns.
How would one write the re-shape operation formally in mathematical notation? Transpose is obviously easy, but is there a parallel for reshapes?
$$mathbf{A} in mathbb{R}^{6times6} rightarrow mathbf{A} in mathbb{R}^{12 times 3}$$
Thx
matrices notation vectors matrix-equations
asked Nov 26 at 15:13
Astrid
283114
Suppose I am coding in python.
Then one can do e.g. something like this:
import numpy as np
A = np.random.rand((6,6))
# Lets reshape it
A_new = A.reshape(-1,3)
So it went from 2D array (matrix) to a 2D array with six 12 rows and three columns.
How would one write the re-shape operation formally in mathematical notation? Transpose is obviously easy, but is there a parallel for reshapes?
$$mathbf{A} in mathbb{R}^{6times6} rightarrow mathbf{A} in mathbb{R}^{12 times 3}$$
Thx
matrices notation vectors matrix-equations
matrices notation vectors matrix-equations
asked Nov 26 at 15:13
Astrid
283114
asked Nov 26 at 15:13
Astrid
283114
asked Nov 26 at 15:13
Astrid
283114
asked Nov 26 at 15:13
Astrid
283114
asked Nov 26 at 15:13
Astrid
283114
283114
add a comment |
add a comment |
1 Answer
1
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The operation $mathbb{R}^{ntimes m}tomathbb{R}^{nm}$ is called vectorization and often is denoted with $mathop{mathrm{vec}}()$. Creating a matrix from vector is an inverse $mathop{mathrm{vec}^{-1}}()$. When one can't deduce what are the dimensions of new matrix, they can be given as sub-indices: $mathop{mathrm{vec}^{-1}_{3,4}}(mathbf v)$ will produce the matrix $3times 4$. To sum up, you can write:
$$
mathop{mathrm{vec}^{-1}_{12,3}}circmathop{mathrm{vec}}: mathbb{R}^{6times 6}tomathbb{R}^{12,3},\
A'= mathop{mathrm{vec}^{-1}_{12,3}}(mathop{mathrm{vec}}(A)).
$$
However, I need to mention, that it isn't a widely used notation, so you are better to introduce it formally beforehand.
Note. There is also a term tensor reshaping, but it's usually referred to an operation of combining dimensions (so no dimension is needed to be a composite integer).
answered Nov 26 at 16:42
Vasily Mitch
1,32837
add a comment |
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1 Answer
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1 Answer
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The operation $mathbb{R}^{ntimes m}tomathbb{R}^{nm}$ is called vectorization and often is denoted with $mathop{mathrm{vec}}()$. Creating a matrix from vector is an inverse $mathop{mathrm{vec}^{-1}}()$. When one can't deduce what are the dimensions of new matrix, they can be given as sub-indices: $mathop{mathrm{vec}^{-1}_{3,4}}(mathbf v)$ will produce the matrix $3times 4$. To sum up, you can write:
$$
mathop{mathrm{vec}^{-1}_{12,3}}circmathop{mathrm{vec}}: mathbb{R}^{6times 6}tomathbb{R}^{12,3},\
A'= mathop{mathrm{vec}^{-1}_{12,3}}(mathop{mathrm{vec}}(A)).
$$
However, I need to mention, that it isn't a widely used notation, so you are better to introduce it formally beforehand.
Note. There is also a term tensor reshaping, but it's usually referred to an operation of combining dimensions (so no dimension is needed to be a composite integer).
answered Nov 26 at 16:42
Vasily Mitch
1,32837
add a comment |
The operation $mathbb{R}^{ntimes m}tomathbb{R}^{nm}$ is called vectorization and often is denoted with $mathop{mathrm{vec}}()$. Creating a matrix from vector is an inverse $mathop{mathrm{vec}^{-1}}()$. When one can't deduce what are the dimensions of new matrix, they can be given as sub-indices: $mathop{mathrm{vec}^{-1}_{3,4}}(mathbf v)$ will produce the matrix $3times 4$. To sum up, you can write:
$$
mathop{mathrm{vec}^{-1}_{12,3}}circmathop{mathrm{vec}}: mathbb{R}^{6times 6}tomathbb{R}^{12,3},\
A'= mathop{mathrm{vec}^{-1}_{12,3}}(mathop{mathrm{vec}}(A)).
$$
However, I need to mention, that it isn't a widely used notation, so you are better to introduce it formally beforehand.
Note. There is also a term tensor reshaping, but it's usually referred to an operation of combining dimensions (so no dimension is needed to be a composite integer).
answered Nov 26 at 16:42
Vasily Mitch
1,32837
add a comment |
The operation $mathbb{R}^{ntimes m}tomathbb{R}^{nm}$ is called vectorization and often is denoted with $mathop{mathrm{vec}}()$. Creating a matrix from vector is an inverse $mathop{mathrm{vec}^{-1}}()$. When one can't deduce what are the dimensions of new matrix, they can be given as sub-indices: $mathop{mathrm{vec}^{-1}_{3,4}}(mathbf v)$ will produce the matrix $3times 4$. To sum up, you can write:
$$
mathop{mathrm{vec}^{-1}_{12,3}}circmathop{mathrm{vec}}: mathbb{R}^{6times 6}tomathbb{R}^{12,3},\
A'= mathop{mathrm{vec}^{-1}_{12,3}}(mathop{mathrm{vec}}(A)).
$$
However, I need to mention, that it isn't a widely used notation, so you are better to introduce it formally beforehand.
Note. There is also a term tensor reshaping, but it's usually referred to an operation of combining dimensions (so no dimension is needed to be a composite integer).
answered Nov 26 at 16:42
Vasily Mitch
1,32837
The operation $mathbb{R}^{ntimes m}tomathbb{R}^{nm}$ is called vectorization and often is denoted with $mathop{mathrm{vec}}()$. Creating a matrix from vector is an inverse $mathop{mathrm{vec}^{-1}}()$. When one can't deduce what are the dimensions of new matrix, they can be given as sub-indices: $mathop{mathrm{vec}^{-1}_{3,4}}(mathbf v)$ will produce the matrix $3times 4$. To sum up, you can write:
$$
mathop{mathrm{vec}^{-1}_{12,3}}circmathop{mathrm{vec}}: mathbb{R}^{6times 6}tomathbb{R}^{12,3},\
A'= mathop{mathrm{vec}^{-1}_{12,3}}(mathop{mathrm{vec}}(A)).
$$
However, I need to mention, that it isn't a widely used notation, so you are better to introduce it formally beforehand.
Note. There is also a term tensor reshaping, but it's usually referred to an operation of combining dimensions (so no dimension is needed to be a composite integer).
answered Nov 26 at 16:42
Vasily Mitch
1,32837
answered Nov 26 at 16:42
Vasily Mitch
1,32837
answered Nov 26 at 16:42
Vasily Mitch
1,32837
answered Nov 26 at 16:42
Vasily Mitch
1,32837
1,32837
add a comment |
add a comment |
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