## The New Encyclopędia BritannicaEncyclopędia Britannica, 1983 - Encyclopedias and dictionaries |

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Page 509

In general, a nonempty set U, the elements of which will be

multiplication of vectors by elements of $ are defined and satisfy 10 postulates (

see ...

In general, a nonempty set U, the elements of which will be

**called**vectors, is**called**a vector space, or a linear space, over a field $ if addition of vectors andmultiplication of vectors by elements of $ are defined and satisfy 10 postulates (

see ...

Page 542

The study of general commutative rings was inaugurated by the German

mathematician Emmy Noe- ther around 1925, with a special emphasis on the

rings that are now

his theory ...

The study of general commutative rings was inaugurated by the German

mathematician Emmy Noe- ther around 1925, with a special emphasis on the

rings that are now

**called**Noetherian. In the second half of the 20th century, withhis theory ...

Page 545

Such an array is

matrix of u with respect to the basis (ft, • • • , e„), denoted M («). Any square nx n

matrix over K is the matrix of some endomorphism u. Because endomorphisms

and ...

Such an array is

**called**a square n x n matrix over K. The matrix is**called**thematrix of u with respect to the basis (ft, • • • , e„), denoted M («). Any square nx n

matrix over K is the matrix of some endomorphism u. Because endomorphisms

and ...

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