Q: What is meant by the word eigenvalue?

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No. Say your matrix is called A, then a number e is an eigenvalue of A exactly when A-eI is singular, where I is the identity matrix of the same dimensions as A. A-eI is singular exactly when (A-eI)T is singular, but (A-eI)T=AT-(eI)T =AT-eI. Therefore we can conclude that e is an eigenvalue of A exactly when it is an eigenvalue of AT.

how does ahp use eigen values and eigen vectors

There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.

If a linear transformation acts on a vector and the result is only a change in the vector's magnitude, not direction, that vector is called an eigenvector of that particular linear transformation, and the magnitude that the vector is changed by is called an eigenvalue of that eigenvector.Formulaically, this statement is expressed as Av=kv, where A is the linear transformation, vis the eigenvector, and k is the eigenvalue. Keep in mind that A is usually a matrix and k is a scalar multiple that must exist in the field of which is over the vector space in question.

The word "meant" has one syllable.

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No.

Yes, it is.

define eigen value problem

Yes it is. In fact, every singular operator (read singular matrix) has 0 as an eigenvalue (the converse is also true). To see this, just note that, by definition, for any singular operator A, there exists a nonzero vector x such that Ax = 0. Since 0 = 0x we have Ax = 0x, i.e. 0 is an eigenvalue of A.

No. Say your matrix is called A, then a number e is an eigenvalue of A exactly when A-eI is singular, where I is the identity matrix of the same dimensions as A. A-eI is singular exactly when (A-eI)T is singular, but (A-eI)T=AT-(eI)T =AT-eI. Therefore we can conclude that e is an eigenvalue of A exactly when it is an eigenvalue of AT.

how does ahp use eigen values and eigen vectors

If a linear transformation acts on a vector and the result is only a change in the vector's magnitude, not direction, that vector is called an eigenvector of that particular linear transformation, and the magnitude that the vector is changed by is called an eigenvalue of that eigenvector.Formulaically, this statement is expressed as Av=kv, where A is the linear transformation, vis the eigenvector, and k is the eigenvalue. Keep in mind that A is usually a matrix and k is a scalar multiple that must exist in the field of which is over the vector space in question.

There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.There is no such word as a "hapliod". If you meant haploid, the answer depends on the species.

There's not nearly enough information here to answer. (Among other things, what the heck is "shere" supposed to be?)The general formula of an eigenvalue equation is Of = Ef. (Sorry, I can't do the normal mathematical notation here, but O is supposed to be an operator, and f is a function of some kind... E is, of course, the eigenvalue). If you know how to do differential equations, the rest is easy (assuming you actually know what O and f are). If you don't, you're not going to understand the answer anyway.

Recall that if a matrix is singular, it's determinant is zero. Let our nxn matrix be called A and let k stand for the eigenvalue. To find eigenvalues we solve the equation det(A-kI)=0for k, where I is the nxn identity matrix. (<==) Assume that k=0 is an eigenvalue. Notice that if we plug zero into this equation for k, we just get det(A)=0. This means the matrix is singluar. (==>) Assume that det(A)=0. Then as stated above we need to find solutions of the equation det(A-kI)=0. Notice that k=0 is a solution since det(A-(0)I) = det(A) which we already know is zero. Thus zero is an eigenvalue.

Synonyms of the word meant are; portent, presage, promise, purport, suggest, symbolize. Antonyms of the word meant are; entail, imply, mean, intend, convey.

Yes, do write. That's what you always have to do when you have got a homework-program.