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Linearization makes it possible to use tools for studying linear systems to analyze the behavior of a nonlinear function near a given point. The linearization of a function is the first order term of its Taylor expansion around the point of interest. For a system defined by the equation
The map x ↦ L(x) is a linear map over any field containing F q.; The set of roots of L is an F q-vector space and is closed under the q-Frobenius map.; Conversely, if U is any F q-linear subspace of some finite field containing F q, then the polynomial that vanishes exactly on U is a linearised polynomial.
In numerical analysis, the local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based on a local (piecewise) linearization of the given equation on consecutive time intervals. The numerical integrators are then iteratively defined as the solution of the resulting piecewise linear ...
A structure of an equivariant sheaf on an invertible sheaf or a line bundle is also called a linearization. Let X be a complete variety over an algebraically closed field acted by a connected reductive group G and L an invertible sheaf on it. If X is normal, then some tensor power of L is linearizable. [4]
This is The Takeaway from today's Morning Brief, which you can sign up to receive in your inbox every morning along with:. The chart of the day. What we're watching. What we're reading. Economic ...
Today's NYT Connections puzzle for Sunday, January 19, 2025The New York Times
Barclays customers are experiencing intermittent errors with payments and transfers for a second day after serious IT problems that also affected the bank's app and online banking.
Linear approximation of a nonlinear system: classification of 2D fixed point according to the trace and the determinant of the Jacobian matrix (the linearization of the system near an equilibrium point). The roots of the characteristic polynomial det(A - λI) are the eigenvalues of A.