Mixing
The fundamental idea behind Linear Algebra
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2
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I'm studying engineering and for the most part, I feel like I understand the main concepts behind Linear Algebra. However, I feel like my understanding is superficial.
I feel like Linear Algebra is a subject that consists of different pieces loosely related to each other, I can't see what the most fundamental idea is behind the subject.
I would really like to know what the main idea is that connects all the different ideas in the subject.
Can someone point me in the right direction? Is it linear transformations? Is it something even deeper? I really want to know.
linear-algebra book-recommendation
edited 3 hours ago
ToposLogos
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asked 4 hours ago
delivosa
905
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up vote
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favorite
I'm studying engineering and for the most part, I feel like I understand the main concepts behind Linear Algebra. However, I feel like my understanding is superficial.
I feel like Linear Algebra is a subject that consists of different pieces loosely related to each other, I can't see what the most fundamental idea is behind the subject.
I would really like to know what the main idea is that connects all the different ideas in the subject.
Can someone point me in the right direction? Is it linear transformations? Is it something even deeper? I really want to know.
linear-algebra book-recommendation
edited 3 hours ago
ToposLogos
1199
asked 4 hours ago
delivosa
905
1
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I'm studying engineering and for the most part, I feel like I understand the main concepts behind Linear Algebra. However, I feel like my understanding is superficial.
I feel like Linear Algebra is a subject that consists of different pieces loosely related to each other, I can't see what the most fundamental idea is behind the subject.
I would really like to know what the main idea is that connects all the different ideas in the subject.
Can someone point me in the right direction? Is it linear transformations? Is it something even deeper? I really want to know.
linear-algebra book-recommendation
edited 3 hours ago
ToposLogos
1199
asked 4 hours ago
delivosa
905
I'm studying engineering and for the most part, I feel like I understand the main concepts behind Linear Algebra. However, I feel like my understanding is superficial.
I feel like Linear Algebra is a subject that consists of different pieces loosely related to each other, I can't see what the most fundamental idea is behind the subject.
I would really like to know what the main idea is that connects all the different ideas in the subject.
Can someone point me in the right direction? Is it linear transformations? Is it something even deeper? I really want to know.
linear-algebra book-recommendation
linear-algebra book-recommendation
edited 3 hours ago
ToposLogos
1199
asked 4 hours ago
delivosa
905
edited 3 hours ago
ToposLogos
1199
asked 4 hours ago
delivosa
905
edited 3 hours ago
ToposLogos
1199
edited 3 hours ago
ToposLogos
1199
edited 3 hours ago
ToposLogos
1199
1199
asked 4 hours ago
delivosa
905
asked 4 hours ago
delivosa
905
asked 4 hours ago
delivosa
905
905
1
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago
add a comment |Â
1
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago
1
1
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
3
down vote
Linear maps, linear spaces, linear dependence, alternating forms and their interrelations.
answered 4 hours ago
timur
11.5k1943
add a comment |Â
up vote
2
down vote
1) The following article is from The Great Soviet Encyclopedia (1979), which sums up the mathematical relations covering subjects of classical Linear Algebra:
Linear Algebra is the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular, quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from finite-dimensional vector spaces to infinite-dimensional linear spaces.
2) A popular and explanatory article: https://betterexplained.com/articles/linear-algebra-guide/
3) There is a fascinating map on the seventh page of the book you should definitely look at https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf
4) Two book recommendations
a) I.M.Gelfand - Lectures on Linear Algebra
b) S. Axler - Linear Algebra Done Right
answered 3 hours ago
ToposLogos
1199
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Linear maps, linear spaces, linear dependence, alternating forms and their interrelations.
answered 4 hours ago
timur
11.5k1943
add a comment |Â
up vote
3
down vote
Linear maps, linear spaces, linear dependence, alternating forms and their interrelations.
answered 4 hours ago
timur
11.5k1943
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Linear maps, linear spaces, linear dependence, alternating forms and their interrelations.
answered 4 hours ago
timur
11.5k1943
Linear maps, linear spaces, linear dependence, alternating forms and their interrelations.
answered 4 hours ago
timur
11.5k1943
answered 4 hours ago
timur
11.5k1943
answered 4 hours ago
timur
11.5k1943
answered 4 hours ago
timur
11.5k1943
11.5k1943
add a comment |Â
add a comment |Â
up vote
2
down vote
1) The following article is from The Great Soviet Encyclopedia (1979), which sums up the mathematical relations covering subjects of classical Linear Algebra:
Linear Algebra is the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular, quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from finite-dimensional vector spaces to infinite-dimensional linear spaces.
2) A popular and explanatory article: https://betterexplained.com/articles/linear-algebra-guide/
3) There is a fascinating map on the seventh page of the book you should definitely look at https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf
4) Two book recommendations
a) I.M.Gelfand - Lectures on Linear Algebra
b) S. Axler - Linear Algebra Done Right
answered 3 hours ago
ToposLogos
1199
add a comment |Â
up vote
2
down vote
1) The following article is from The Great Soviet Encyclopedia (1979), which sums up the mathematical relations covering subjects of classical Linear Algebra:
Linear Algebra is the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular, quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from finite-dimensional vector spaces to infinite-dimensional linear spaces.
2) A popular and explanatory article: https://betterexplained.com/articles/linear-algebra-guide/
3) There is a fascinating map on the seventh page of the book you should definitely look at https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf
4) Two book recommendations
a) I.M.Gelfand - Lectures on Linear Algebra
b) S. Axler - Linear Algebra Done Right
answered 3 hours ago
ToposLogos
1199
add a comment |Â
up vote
2
down vote
up vote
2
down vote
1) The following article is from The Great Soviet Encyclopedia (1979), which sums up the mathematical relations covering subjects of classical Linear Algebra:
Linear Algebra is the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular, quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from finite-dimensional vector spaces to infinite-dimensional linear spaces.
2) A popular and explanatory article: https://betterexplained.com/articles/linear-algebra-guide/
3) There is a fascinating map on the seventh page of the book you should definitely look at https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf
4) Two book recommendations
a) I.M.Gelfand - Lectures on Linear Algebra
b) S. Axler - Linear Algebra Done Right
answered 3 hours ago
ToposLogos
1199
1) The following article is from The Great Soviet Encyclopedia (1979), which sums up the mathematical relations covering subjects of classical Linear Algebra:
Linear Algebra is the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular, quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from finite-dimensional vector spaces to infinite-dimensional linear spaces.
2) A popular and explanatory article: https://betterexplained.com/articles/linear-algebra-guide/
3) There is a fascinating map on the seventh page of the book you should definitely look at https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf
4) Two book recommendations
a) I.M.Gelfand - Lectures on Linear Algebra
b) S. Axler - Linear Algebra Done Right
answered 3 hours ago
ToposLogos
1199
answered 3 hours ago
ToposLogos
1199
answered 3 hours ago
ToposLogos
1199
answered 3 hours ago
ToposLogos
1199
1199
add a comment |Â
add a comment |Â
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1
The “Essence of linear algebra†video series by 3Blue1Brown might be helpful (even though it's perhaps a longer answer than what you're looking for here): youtube.com/watch?v=kjBOesZCoqc
– Hans Lundmark
4 hours ago
See math.stackexchange.com/questions/615017/…
– lhf
4 hours ago
Most of linear algebra can be motivated with geometry and pictures. What exactly are the "loose pieces" that you have in mind?
– rschwieb
2 hours ago