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Golub mentioned secular equation in his matrix computation and a slide You should end up with a quadratic. However i still don't get its definition

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How is a secular equation defined For every homogeneous fredholm equation, there is an associated secular equation you need to solve to find the eigenvalues How can one identify secular terms while doing multiscale expansion

In an initial value problem, can any term where t appears can be counted as secular term?

I found a definition of regular matrices that is, a regular matrix $a$ is a square matrix and there are some n ($\\geq$1) such that all the entries of $a^n$ are. On the other hand, the definition of a regular surface is given by saying that it is a subset of $\mathbb r^3$ with all the standard properties. I was wondering if a dot product is technically a term used when discussing the product of $2$ vectors is equal to $0$ And would anyone agree that an inner product is a term used when discussing.

So what will be definition of regular map between open subset of some affine space to open subset of another affine space Shaferevich does not define this he we dont regard this as quasiprojective. If you're trying to define what it means for a function to be regular on an open subset of an affine variety, you must you definition 2 There are only two situations that i am aware of that give rise to extraneous roots, namely, the “square both sides” situation (in order to eliminate a square root symbol), and the “half absolute v.