Mixing
Book about geometric meaning of matrices and their operations
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Is there a book (e.g. linear algebra book, or maybe geometry book) that explains in great details the geometric meaning of matrices and the effect of operations on them?
I’m not simply talking about a book with a few illustrations for what a rotation does to the plane.
Here is the kind of questions I wish the book answered:
For instance, determinant is area multiplier.
Another example: any matrix can be seen as a rotation, scaling then another rotation. This is what SVD decomposition tells us.
But what is the transpose of a matrix? What’s the geometric effect? Once again SVD, tells us that this is inverse rotations but same scaling. Any other way to understand or “see” this ?
linear-algebra geometry reference-request book-recommendation matrix-calculus
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
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add a comment |
$begingroup$
Is there a book (e.g. linear algebra book, or maybe geometry book) that explains in great details the geometric meaning of matrices and the effect of operations on them?
I’m not simply talking about a book with a few illustrations for what a rotation does to the plane.
Here is the kind of questions I wish the book answered:
For instance, determinant is area multiplier.
Another example: any matrix can be seen as a rotation, scaling then another rotation. This is what SVD decomposition tells us.
But what is the transpose of a matrix? What’s the geometric effect? Once again SVD, tells us that this is inverse rotations but same scaling. Any other way to understand or “see” this ?
linear-algebra geometry reference-request book-recommendation matrix-calculus
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
$endgroup$
$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47
add a comment |
$begingroup$
Is there a book (e.g. linear algebra book, or maybe geometry book) that explains in great details the geometric meaning of matrices and the effect of operations on them?
I’m not simply talking about a book with a few illustrations for what a rotation does to the plane.
Here is the kind of questions I wish the book answered:
For instance, determinant is area multiplier.
Another example: any matrix can be seen as a rotation, scaling then another rotation. This is what SVD decomposition tells us.
But what is the transpose of a matrix? What’s the geometric effect? Once again SVD, tells us that this is inverse rotations but same scaling. Any other way to understand or “see” this ?
linear-algebra geometry reference-request book-recommendation matrix-calculus
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
$endgroup$
Is there a book (e.g. linear algebra book, or maybe geometry book) that explains in great details the geometric meaning of matrices and the effect of operations on them?
I’m not simply talking about a book with a few illustrations for what a rotation does to the plane.
Here is the kind of questions I wish the book answered:
For instance, determinant is area multiplier.
Another example: any matrix can be seen as a rotation, scaling then another rotation. This is what SVD decomposition tells us.
But what is the transpose of a matrix? What’s the geometric effect? Once again SVD, tells us that this is inverse rotations but same scaling. Any other way to understand or “see” this ?
linear-algebra geometry reference-request book-recommendation matrix-calculus
linear-algebra geometry reference-request book-recommendation matrix-calculus
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
edited Jan 23 at 12:09
Julien__
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
asked Jan 22 at 16:23
Julien__Julien__
1,2932819
1,2932819
$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47
add a comment |
$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47
$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47
$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47
add a comment |
1 Answer
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The following might not be exactly what you're looking for but I personally find Chapter 2: Geometry of Linear Maps, from J. Callahan: Advanced Calculus. A Geometric View, Springer 2010, a very nice intro to the topic on just 42 pages.
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
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1 Answer
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$begingroup$
The following might not be exactly what you're looking for but I personally find Chapter 2: Geometry of Linear Maps, from J. Callahan: Advanced Calculus. A Geometric View, Springer 2010, a very nice intro to the topic on just 42 pages.
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
$endgroup$
add a comment |
$begingroup$
The following might not be exactly what you're looking for but I personally find Chapter 2: Geometry of Linear Maps, from J. Callahan: Advanced Calculus. A Geometric View, Springer 2010, a very nice intro to the topic on just 42 pages.
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
$endgroup$
add a comment |
$begingroup$
The following might not be exactly what you're looking for but I personally find Chapter 2: Geometry of Linear Maps, from J. Callahan: Advanced Calculus. A Geometric View, Springer 2010, a very nice intro to the topic on just 42 pages.
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
$endgroup$
The following might not be exactly what you're looking for but I personally find Chapter 2: Geometry of Linear Maps, from J. Callahan: Advanced Calculus. A Geometric View, Springer 2010, a very nice intro to the topic on just 42 pages.
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
answered Jan 22 at 16:39
Roman HricRoman Hric
1365
1365
add a comment |
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$begingroup$
You'll be better informed through the superb work of 3blue1brown, such as here: youtube.com/watch?v=kYB8IZa5AuE and related ones. Enjoy!
$endgroup$
– David G. Stork
Jan 22 at 17:47