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Is eigenvalue applicable only to n x n matrices?
The answer is yes, and here's why: Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds: M.v = k*v, where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix. For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix. Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.
What word is used for the answer to a division problem?
The answer to a division problem is called a quotient or divide. The answer to a division problem is called a quotient or divide.
Is the sum in problem?
The sum is the answer in an addition problem.
What is a hypothetical problem?
A hypothetical problem is a problem that has not yet actually happened. Usually hypothetical problems are discussed in order to prepare for the problem, should it occur.
What do you call the answer to subtraction problem?
The answer in a subtraction problem is difference.
What has the author Gillian Frances Colkin written?
Gillian Frances Colkin has written: 'The location of roots of equations with particular reference to the generalized eigenvalue problem'
Is eigenvalue of any operator must be real?
No.
Is lambda 2 an eigenvalue of 33 28?
Yes, it is.
Is there exist a matrix whose eigenvalues are different that of its transpose?
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.
What has the author Anurag Gupta written?
Anurag Gupta has written: 'Krylov sub-space methods for K-eigenvalue problem in 3-D multigroup neutron transport' -- subject(s): Neutron transport theory
What has the author Ricardo Macias Carrasco written?
Ricardo Macias Carrasco has written: 'The eigenvalue problem in the OL/2 language' -- subject(s): Data processing, Eigenvalues, OL/2 (Computer program language)
How does AHP use eigenvalue and eigenvector?
how does ahp use eigen values and eigen vectors
What is an eigenvalue?
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.
Is 0 an eigenvalue?
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.
What is meant by the word eigenvalue?
The term "eigenvalue" refers to a noun which means each set of values of parameter for which differential equation has a nonzero solution. It can also refers to any number such that given matrix subtracted by the same number and multiply to the identity matrix has a zero determinant.
How do you get eigenvalue of sphere as 0.99999987 Want formula to calculate it?
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.
Prove that a matrix a is singular if and only if it has a zero eigenvalue?
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.
