Rank-nullity theorem — The rank-nullity theorem states that for any linear map where is finite-dimensional, the dimension of equals the sum of the map's rank and nullity. [1] [2] [3]
Observations
- One
- Two
- Three
Every linear injection has a left-inverse.
Every linear surjection has a right-inverse.
There is hardly any theory which is more elementary [than linear algebra], in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices.
— Jean Dieudonné, Treatise on Analysis, Volume 1
We share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.
— Irving Kaplansky, in writing about Paul Halmos
Rank-nullity theorem — The rank-nullity theorem states that for any linear map where is finite-dimensional, the dimension of equals the sum of the map's rank and nullity. [1] [2] [3]
Observations
- One
- Two
- Three
Every linear injection has a left-inverse.
Every linear surjection has a right-inverse.
There is hardly any theory which is more elementary [than linear algebra], in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices.
— Jean Dieudonné, Treatise on Analysis, Volume 1
We share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.
— Irving Kaplansky, in writing about Paul Halmos