binet formula造句

• Given these three roots, the Perrin sequence analogue of the Lucas sequence Binet formula is
• There are various kinds of proofs that can be given for the Cauchy " Binet formula.
• In 1765, Leonhard Euler published an explicit formula, known today as the Binet formula,
• The formula can be generalized to ( square ) products of rectangular matrices, giving the Cauchy Binet formula, which also provides an independent proof of the multiplicative property.
• From the moment of Binet and Lucas works ( 19 c . ) Fibonacci-mathematicians did not notice Binet formulas and not interpret them as a new class of hyperbolic functions.
• It is difficult to assume that the editorial board of 玊he Fibonacci Quarterly " did not know Binet formulas and Lucas article ( 1878 ), which was published by the Fibonacci Association in 1969
• If all elements of these matrices would commute then one knows that the determinant of " E " can be expressed by the so-called Cauchy Binet formula via minors of " X " and " D ".
• Thus one can work out both sides of the Cauchy " Binet formula by linearity for every row of " A " and then also every column of " B ", writing each of the rows and columns as a linear combination of standard basis vectors.
• The resulting multiple summations are huge, but they have the same form for both sides : corresponding terms involve the same scalar factor ( each is a product of entries of " A " and of " B " ), and these terms only differ by involving two different expressions in terms of constant matrices of the kind described above, which expressions should be equal according to the Cauchy " Binet formula.
• On the same day ( November 30, 1812 ) that Binet presented his paper to the Academy, Cauchy also presented one on the subject . ( See Cauchy Binet formula . ) In this he used the word " "'determinant " "'in its present sense, summarized and simplified what was then known on the subject, improved the notation, and gave the multiplication theorem with a proof more satisfactory than Binet's.
• Now, if we compare the coefficient of z ^ { n-m } in the equation \ det ( zI _ n + BA ) = z ^ { n-m } \ det ( zI _ m + AB ), the left hand side will give the sum of the principal minors of BA while the right hand side will give the constant term of \ det ( zI _ m + AB ), which is simply \ det ( AB ), which is what the Cauchy Binet formula states, i . e.