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| Somebody (myself, if I'll win the laziness) should add something about the formal definition of determinant (an alternating function of the rows or columns etc. ...), of which its unicity and how to compute it are consequences. --] | Somebody (myself, if I'll win the laziness) should add something about the formal definition of determinant (an alternating function of the rows or columns etc. ...), of which its unicity and how to compute it are consequences. --] | ||
| ...and add to that the foundation of the definition, which is something to do with multilinear functions.<br> | ...and add to that the foundation of the definition, which is something to do with multilinear functions.<br> | ||
| Also worth mentioning that historically, the concept of determinant came ''before'' the matrix. | Also worth mentioning that historically, the concept of determinant came ''before'' the matrix. | ||
| :That would certainly be very interesting. What is the history of the concept? --AxelBoldt | :That would certainly be very interesting. What is the history of the concept? --AxelBoldt | ||
| ⚫ | I'll see what I can dig up, but briefly: a determinant was originally a property of a system of equations. When the idea of putting co-efficients into a grid came up, the term "matrix" was coined to mean "mother of the determinant", as in womb. | ||
| ⚫ | I'll see what I can dig up, but briefly: a determinant was originally a property of a system of equations. When the idea of putting co-efficients into a grid came up, the term "matrix" was coined to mean "mother of the determinant". | ||
| <br> | <br> | ||
| ⚫ | The determinant function is defined in terms of vector spaces. It is the only function f: F^n x F^n .... x F^n -> F that is multilinear & alternating such that f( standard basis ) = 1.<br> | ||
| ⚫ | The determinant function is defined in terms of vector spaces. It is the only function F^n x F^n .... x F^n -> F that is multilinear & alternating such that f( standard basis ) = 1.<br> | ||
| Obviously, the above needs a major amount of fleshing out.... | Obviously, the above needs a major amount of fleshing out.... | ||
Revision as of 15:43, 25 February 2002
Somebody (myself, if I'll win the laziness) should add something about the formal definition of determinant (an alternating function of the rows or columns etc. ...), of which its unicity and how to compute it are consequences. --Goochelaar
...and add to that the foundation of the definition, which is something to do with multilinear functions.
Also worth mentioning that historically, the concept of determinant came before the matrix.
- That would certainly be very interesting. What is the history of the concept? --AxelBoldt
I'll see what I can dig up, but briefly: a determinant was originally a property of a system of equations. When the idea of putting co-efficients into a grid came up, the term "matrix" was coined to mean "mother of the determinant", as in womb.
The determinant function is defined in terms of vector spaces. It is the only function f: F^n x F^n .... x F^n -> F that is multilinear & alternating such that f( standard basis ) = 1.
Obviously, the above needs a major amount of fleshing out....