A Solution of the Matric Equation P(X) |
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Page 585
... members of ( 9 ) with respect to A , and we find ¥ í ( P ) P ' ( x ) = { øx ( X ) Q1 ( A ) } ' . Substitute B for λ in this identity ; since e , > 1 , the right member is zero and we have Ví ( a , ) P ' ( BKT ) = 0 . Now ( λ - ẞk ) , e ...
... members of ( 9 ) with respect to A , and we find ¥ í ( P ) P ' ( x ) = { øx ( X ) Q1 ( A ) } ' . Substitute B for λ in this identity ; since e , > 1 , the right member is zero and we have Ví ( a , ) P ' ( BKT ) = 0 . Now ( λ - ẞk ) , e ...
Page 586
... 0 , where r≤ -1 ; then letting λ = ẞr in ( 13 ) , the right member will be zero for ( - ) is a factor of ( X ) and because of the relations just written and because of ( 11 ) , we must likewise have 4 ) ( α , ) = 0 . -- Then ( -a ) +1 ...
... 0 , where r≤ -1 ; then letting λ = ẞr in ( 13 ) , the right member will be zero for ( - ) is a factor of ( X ) and because of the relations just written and because of ( 11 ) , we must likewise have 4 ) ( α , ) = 0 . -- Then ( -a ) +1 ...
Page 588
... member by Hx ( ^ ) ox ( ^ ) + T1 ( P ) according to ( 19 ) , we obtain the identity or - P ( X ) — α , = P ( Tx ( P ) ... 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 ...
... member by Hx ( ^ ) ox ( ^ ) + T1 ( P ) according to ( 19 ) , we obtain the identity or - P ( X ) — α , = P ( Tx ( P ) ... 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 ...
Common terms and phrases
a₁ algebra B₁ bilineare Formen bilinearen binomial equation Cecioni characteristic equation characteristic function column Comptes Rendus consequently constants t1 corresponding Crelle's Journal degree in common degree m>1 distinct roots elementary divisors equation of lowest equation P(X expressible as polynomials 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 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 Substitute Substitutionen und bilineare Sylvester t₁ T₂ theory UNIVERSITY OF WISCONSIN Weierstrass X₁ X²=A Zürich βρε λ² λ³