Results 301 to 310 of about 6,615,701 (321)
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Linear Systems and Polynomials
1984One of the main applications of polynomial theory occurs in the analysis of linear electrical circuits and the many other physical situations that are customarily represented by linear-circuit analogs. With the advent of computers and digital signal processing, time-discrete systems have taken on a special significance, and these are effectively ...
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1959
We shall consider first linear differential systems $$ {x_{i}}' = \sum\limits_{{j = 1}}^{n} {{a_{{ij}}}(t){x_{j}}\quad } i = 1,...,n, $$ (3.1.1) i.e., x’ = A(t)x, x = (x1..., x n ), A(t) = [aij(t)], and linear differential equations $$ {x^{{(n)}}} + {a_{1}}(t)\;{x^{{(n - 1)}}} + ... + {a_{n}}(t)\;x = 0, $$ (3.1.2) whose coefficients
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We shall consider first linear differential systems $$ {x_{i}}' = \sum\limits_{{j = 1}}^{n} {{a_{{ij}}}(t){x_{j}}\quad } i = 1,...,n, $$ (3.1.1) i.e., x’ = A(t)x, x = (x1..., x n ), A(t) = [aij(t)], and linear differential equations $$ {x^{{(n)}}} + {a_{1}}(t)\;{x^{{(n - 1)}}} + ... + {a_{n}}(t)\;x = 0, $$ (3.1.2) whose coefficients
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Linear Transformations and Linear Systems
2020Machine learning algorithms work with data matrices, which can be viewed as collections of row vectors or as collections of column vectors. For example, one can view the rows of an n × d data matrix D as a set of n points in a space of dimensionality d, and one can view the columns as features. These collections of row vectors and column vectors define
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1978
In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important roles. A system of linear equations has the form $$\begin{gathered} {{a}_{{1,1}}}{{x}_{1}} + {{a}_{{1,2}}}{{x}_{2}} + \cdots + {{a}_{{1,n}}}{{x}_{n}} = {{b}_{1}}, \hfill \\ {{a}_{{2,1}
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In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important roles. A system of linear equations has the form $$\begin{gathered} {{a}_{{1,1}}}{{x}_{1}} + {{a}_{{1,2}}}{{x}_{2}} + \cdots + {{a}_{{1,n}}}{{x}_{n}} = {{b}_{1}}, \hfill \\ {{a}_{{2,1}
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1964
1. Unter einer algebraischen Gleichung n-ten Grades in x versteht man ein gleich Null gesetztes Polynom n-ten Grades in x worin die Koeffizienten A0, Al, ..., An bekannte reelle Zahlen und An ≠ 0 sein sollen. 2. Eine Zahl xl heist Losung (Wurzel) der Gleichung, wenn sie diese identisch erfullt:
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1. Unter einer algebraischen Gleichung n-ten Grades in x versteht man ein gleich Null gesetztes Polynom n-ten Grades in x worin die Koeffizienten A0, Al, ..., An bekannte reelle Zahlen und An ≠ 0 sein sollen. 2. Eine Zahl xl heist Losung (Wurzel) der Gleichung, wenn sie diese identisch erfullt:
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