A Solution of the Matric Equation P(X) |
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Page 581
... 0 , which may or may not be the equation of lowest degree satisfied by A ... roots of ( x ) = 0 are a ;, j = 1 , 2 , . . . , s ; if P ( X ) is a polynomial inλ of degree p > 1 , whose leading coefficient is unity and ... EQUATION P ( X ) = A.
... 0 , which may or may not be the equation of lowest degree satisfied by A ... roots of ( x ) = 0 are a ;, j = 1 , 2 , . . . , s ; if P ( X ) is a polynomial inλ of degree p > 1 , whose leading coefficient is unity and ... EQUATION P ( X ) = A.
Page 582
... roots of ( X ) = 0 and where - ; = m . We have , by hypothesis , ( 2 ) P ( A ) = XP + h1λP - 1 + h2λP - 2 + ··· + hp - 1d ; • and we assume further that P ( X ) ... 0 , ... , s . From ( 1 ) and ( 3 ) , it follows that j = 1 , 2 , 4 ( P ( x ) ) ...
... roots of ( X ) = 0 and where - ; = m . We have , by hypothesis , ( 2 ) P ( A ) = XP + h1λP - 1 + h2λP - 2 + ··· + hp - 1d ; • and we assume further that P ( X ) ... 0 , ... , s . From ( 1 ) and ( 3 ) , it follows that j = 1 , 2 , 4 ( P ( x ) ) ...
Page 583
... roots of each equation P ( X ) -a ; = 0 , j = 1 , 2 , ... , s , in a separate column thus : - — = P ( X ) α10 , P ... EQUATION P ( X ) = A.
... roots of each equation P ( X ) -a ; = 0 , j = 1 , 2 , ... , s , in a separate column thus : - — = P ( X ) α10 , P ... EQUATION P ( X ) = A.
Page 588
... ( X ) = A THEOREM III . If ¥ ( X ) is a polynomial of degree m > 1 in λ , and the distinct roots of ( x ) = 0 are a ;, j = 1 , 2 , ... , s ; if P ( X ) is a polynomial of degree p > 1 in λ whose leading coefficient is unity and whose constant ...
... ( X ) = A THEOREM III . If ¥ ( X ) is a polynomial of degree m > 1 in λ , and the distinct roots of ( x ) = 0 are a ;, j = 1 , 2 , ... , s ; if P ( X ) is a polynomial of degree p > 1 in λ whose leading coefficient is unity and whose constant ...
Page 591
... 0 , since P ( X ) = A and F ( X ) = 0 . But V ( A ) is a polynomial of ... roots of the equation ( X ) = 0 , where ¥ ( X ) is the polynomial of lowest degree for which ¥ ( A ) = 0 , and where p ; is the number of ... EQUATION P ( X ) = A.
... 0 , since P ( X ) = A and F ( X ) = 0 . But V ( A ) is a polynomial of ... roots of the equation ( X ) = 0 , where ¥ ( X ) is the polynomial of lowest degree for which ¥ ( A ) = 0 , and where p ; is the number of ... EQUATION P ( X ) = A.
Common terms and phrases
a₁ algebra bilineare Formen bilinearen binomial equation Cecioni characteristic equation characteristic function column Comptes Rendus consequently constants t1 corresponding Crelle's Journal degree m>1 distinct roots equation A)=0 equation of lowest equation P(X equation X²=A expressible as polynomials factor A-a factor in common factor of 1(A field F Frobenius given matrix h₁ h₂ identity 9 Ingraham Kreis least one simple linearly independent lowest degree satisfied Mathematical Papers matrix of order members of 9 method multiple factor multiple root non-singular number of distinct number of simple polynomial ₁ polynomial of degree polynomial of lowest polynomial P(X present theorem quadratic factor quaternions right member root of X)=0 roots of P(X satisfies the identity scalar coefficients second degree simple root singular matrix solution obtained square matrix ßkr Substitute Substitutionen und bilineare Sylvester t₁ T₂ theory UNIVERSITY OF WISCONSIN Weierstrass X₁ Zürich Þ½ λ² λ³ μ₁