Example sentences of "can be [vb pp] as [art] product " in BNC.
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| 1 | The very subject matter of ‘ Kubla Khan ’ , Xanadu , is heavily connotated with creativity , since it was to be Kubla 's invention , a mythical city based entirely on his own personal ideas , and to some extent , it can be seen as a product of his own imagination blended with the awesome power which he wields ( needed in order to create such a setting ) . |
| 2 | Then a can be expressed as a product of finitely many positive irreducibles ( i.e. primes ) . |
| 3 | Theorem 1.5.1 ( The Unique Factorisation Theorem for Z ; also called the Fundamental Theorem of Arithmetic ) Let a be a non-zero element of Z. Then either a is a unit or a can be expressed as a product of a unit and finitely may positive primes . |
| 4 | Proof Half of the theorem has been proved already ; Lemma 1.3.9 and Remark ( ii ) following it show that every integer greater than 1 ( respectively , less than -1 ) can be expressed as a product of ( respectively , -1 times a product of ) finitely many positive irreducibles ( which we now know to be primes ) . |
| 5 | ( iii ) As we did with the integers ( 1.3.9 ) we can use induction ( but this time on the degree ) to show that every non-zero non-unit polynomial in Q[x] can be expressed as a product of a finite number of irreducible ones . |
| 6 | Then either f is a unit or f can be expressed as a product of a unit and finitely many monic * irreducible polynomials . |
| 7 | Applying this to R[x] we get Theorem 1.11.9 If f ε R[x] then f can be expressed as a product of polynomials of degrees at most 2 in R[x] . |
| 8 | If now we postmultiply the ( 3 × 2 ) submatrix of A by I , we can add the last result to it to recover A as the matrix product unc Finally , a matrix of rank 1 can be expressed as the product of a column and a row in that order — for such a matrix has effectively only one independent column , all the other columns being proportional to it ; similarly for the rows . |
| 9 | Theorem V — Any matrix can be expressed as the product of two symmetric matrices . |
| 10 | By 1.3.9 , Nn can be written as a product of finitely many primes [ i.e. irreducibles ] unc say , where each ti must be one of the primes from the complete list |
| 11 | ( i ) If A is not symmetric , but can be written as the product |
| 12 | It is a simple matter , which we leave to the reader , to show that if A is real , symmetric and positive definite , then it can be written as the product BTB where B is real and triangular . |
| 13 | I would suggest that this attention to differences between context-dependent and objective description can be explained as a product of the specific academic tradition to which these writers are the heirs . |
| 14 | Singular matrices can be factorised as the product of two rectangular matrices — again , in more ways than one — the orders of which are determined by the rank of the matrix . |