3 ms·

You should reread the post. The author lays out a couple of interesting properties and derives the function that satisfies them. It turns out that this function

by acomar 13y ago

You should reread the post. The author lays out a couple of interesting properties and derives the function that satisfies them. It turns out that this function is the usual determinant. Then he shows some examples of applying this new intuition.

VLM 13y ago
Not getting it. What makes it weird? Its like listening to people talk about "power" WRT computers unless they know ohms law, you'd think there's gun barrels in there or little politicians.
- acomar 13y ago
  Weird is in the eye of the beholder. Let me put it this way, do you understand why matrix multiplication is defined the way it is? That looks weird too if you've never tried to derive it for yourself. That is, it's the lack of intuition and familiarity with the underlying concepts (vector algebra) that make it look weird. Also, the question is about a formula. The determinant is a function from a matrix to a scalar that behaves in a nice way. The motivation for the particular properties chosen for "nice"-ness are complicated and out of the scope of the author's answer. But the idea is that you want some number that can represent the matrix in certain contexts (exactly the contexts defined by the listed properties). From there, you just go through the derivation laid out in the OP and you wind up with a computable function. That's where the determinant comes from, that's why it's "weird", etc.. It's a derived function. It just so happens that there are other emergent properties that make it rather useful for doing practical things with matrices. > Its like listening to people talk about "power" WRT computers unless they know ohms law, you'd think there's gun barrels in there or little politicians. I don't follow, the argument presented in the OP is semi-rigorous; words are chosen carefully and used with their usual mathematical definitions, not with the intuitive English definitions.

by acomar 13y ago

VLM 13y ago

Not getting it. What makes it weird? Its like listening to people talk about "power" WRT computers unless they know ohms law, you'd think there's gun barrels in there or little politicians.

acomar 13y ago
Weird is in the eye of the beholder. Let me put it this way, do you understand why matrix multiplication is defined the way it is? That looks weird too if you've never tried to derive it for yourself. That is, it's the lack of intuition and familiarity with the underlying concepts (vector algebra) that make it look weird. Also, the question is about a formula. The determinant is a function from a matrix to a scalar that behaves in a nice way. The motivation for the particular properties chosen for "nice"-ness are complicated and out of the scope of the author's answer. But the idea is that you want some number that can represent the matrix in certain contexts (exactly the contexts defined by the listed properties). From there, you just go through the derivation laid out in the OP and you wind up with a computable function. That's where the determinant comes from, that's why it's "weird", etc.. It's a derived function. It just so happens that there are other emergent properties that make it rather useful for doing practical things with matrices. > Its like listening to people talk about "power" WRT computers unless they know ohms law, you'd think there's gun barrels in there or little politicians. I don't follow, the argument presented in the OP is semi-rigorous; words are chosen carefully and used with their usual mathematical definitions, not with the intuitive English definitions.