Exposition of Basis Free Linear Algebra
Clash Royale CLAN TAG#URR8PPP
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I am looking for a text on linear algebra which is entirely basis free, and makes heavy use of the exterior algebra.
For instance, let $V$ be an $n$-dimensional vector space over a field $k$. Determinant of a map $phi : V rightarrow V$ may be defined as the map $Lambda^n V stackrelLambda^n (phi)rightarrow Lambda^n V$, which is a scalar after choosing any basis of the one dimensional space $Lambda^n V$. I am looking for a textbook which covers linear algebra in terms such as this.
linear-algebra reference-request
asked Sep 3 at 8:40
Dean Young
1,430719
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up vote
1
down vote
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I am looking for a text on linear algebra which is entirely basis free, and makes heavy use of the exterior algebra.
For instance, let $V$ be an $n$-dimensional vector space over a field $k$. Determinant of a map $phi : V rightarrow V$ may be defined as the map $Lambda^n V stackrelLambda^n (phi)rightarrow Lambda^n V$, which is a scalar after choosing any basis of the one dimensional space $Lambda^n V$. I am looking for a textbook which covers linear algebra in terms such as this.
linear-algebra reference-request
asked Sep 3 at 8:40
Dean Young
1,430719
I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am looking for a text on linear algebra which is entirely basis free, and makes heavy use of the exterior algebra.
For instance, let $V$ be an $n$-dimensional vector space over a field $k$. Determinant of a map $phi : V rightarrow V$ may be defined as the map $Lambda^n V stackrelLambda^n (phi)rightarrow Lambda^n V$, which is a scalar after choosing any basis of the one dimensional space $Lambda^n V$. I am looking for a textbook which covers linear algebra in terms such as this.
linear-algebra reference-request
asked Sep 3 at 8:40
Dean Young
1,430719
I am looking for a text on linear algebra which is entirely basis free, and makes heavy use of the exterior algebra.
For instance, let $V$ be an $n$-dimensional vector space over a field $k$. Determinant of a map $phi : V rightarrow V$ may be defined as the map $Lambda^n V stackrelLambda^n (phi)rightarrow Lambda^n V$, which is a scalar after choosing any basis of the one dimensional space $Lambda^n V$. I am looking for a textbook which covers linear algebra in terms such as this.
linear-algebra reference-request
linear-algebra reference-request
asked Sep 3 at 8:40
Dean Young
1,430719
asked Sep 3 at 8:40
Dean Young
1,430719
asked Sep 3 at 8:40
Dean Young
1,430719
asked Sep 3 at 8:40
Dean Young
1,430719
asked Sep 3 at 8:40
Dean Young
1,430719
1,430719
I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05
add a comment |Â
I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05
I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05
add a comment |Â
1 Answer
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This pdf file looks rather interesting, although it is probably just a university report. It was published by the author through lulu.com: buy the book.
answered Sep 3 at 9:17
Siminore
29.9k23167
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
This pdf file looks rather interesting, although it is probably just a university report. It was published by the author through lulu.com: buy the book.
answered Sep 3 at 9:17
Siminore
29.9k23167
add a comment |Â
up vote
3
down vote
accepted
This pdf file looks rather interesting, although it is probably just a university report. It was published by the author through lulu.com: buy the book.
answered Sep 3 at 9:17
Siminore
29.9k23167
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
This pdf file looks rather interesting, although it is probably just a university report. It was published by the author through lulu.com: buy the book.
answered Sep 3 at 9:17
Siminore
29.9k23167
This pdf file looks rather interesting, although it is probably just a university report. It was published by the author through lulu.com: buy the book.
answered Sep 3 at 9:17
Siminore
29.9k23167
answered Sep 3 at 9:17
Siminore
29.9k23167
answered Sep 3 at 9:17
Siminore
29.9k23167
answered Sep 3 at 9:17
Siminore
29.9k23167
29.9k23167
add a comment |Â
add a comment |Â
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I think you are mixing some things up in the definition of your determinant there, i.e. I would like to see a proof that the determinant can be uniquely determined/defined by a map between two one dimensional spaces, in this case $Lambda^n V$...
– Dirk Liebhold
Sep 3 at 9:23
Would this answer your question? math.stackexchange.com/questions/21614/…
– Dean Young
Sep 3 at 21:05