We [he and Halmos] share a philosophy about linear…
![“We [he and Halmos] 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.” quote by Irving Kaplansky](https://sms4smile.com/q/img-quotes/412/irving-kaplansky-103422_algebra_we-he-and-halmos-share-a-philosophy-abou_1805230.png)
“We [he and Halmos] 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.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
In linear algebra, they prefer abstract, basis‑free thinking but resort to concrete matrix calculations when needed.
In simple terms: Think abstractly, compute concretely when required.
Key Takeaway
Balance theory with practice.
Themes
mathematics
linear algebra
abstraction
computation
collaboration
Mood
analytical
practical
Type
letter
philosophical statement
When to use this quote
- research work
- teaching
- problem solving sessions
Key Concepts
basis‑free
matrices
theory
practicality
problem solving
Questions to Reflect On
- When is abstraction insufficient?
- How does concrete computation aid insight?
A Different Perspective
May undervalue computational tools.