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Oh, dude, an eigenvector is like a fancy term in math for a vector that doesn't change direction when a linear transformation is applied to it. It's basically a vector that just chills out and stays the same way, no matter what you do to it. So, yeah, eigenvectors are like the cool, laid-back dudes of the math world.
What else can I help you with?
What is the echelon of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What are the entries of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What are eigenvalues and eigenvectors?
An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.
How does AHP use eigenvalue and eigenvector?
how does ahp use eigen values and eigen vectors
What is the relationship between eigenvalue and mutual information?
I'm seeking the answer too. What's the meaning of the principal eigenvector of an MI matrix?
What is the significance of the unit eigenvector in the context of linear algebra and eigenvalues?
In linear algebra, the unit eigenvector is important because it represents a direction in which a linear transformation only stretches or shrinks, without changing direction. It is associated with an eigenvalue, which tells us the amount of stretching or shrinking that occurs in that direction. This concept is crucial for understanding how matrices behave and for solving systems of linear equations.
What is the echelon of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What are the eignvalues of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What are the entries of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What is equality of a matrix?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
What are eigen values and eigen vectors?
This is a complicated subject, which can't be explained in a few words. Read the Wikipedia article on "eigenvalue"; or better yet, read a book on linear algebra. Briefly, and quoting from the Wikipedia, "The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix."
What Albert Einstein invent in math?
He used EigenVector spaces in a unique way, that is still hard to this day to understand. See: http://www.einstein-online.info/spotlights/path_integrals
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.
What has the author S Srinathkumar written?
S Srinathkumar has written: 'Eigenvalue/eigenvector assignment using output feedback' -- subject(s): Mathematical models, Control systems, Airplanes
What is the -matrix of groups-identity of matrix-inverse matrix-multiplication of matrices?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
How eigenvalues are calculated?
An eigenvector of a square matrix Ais a non-zero vector v that, when the matrix is multiplied by v, yields a constant multiple of v, the multiplier being commonly denoted by lambda. That is: Av = lambdavThe number lambda is called the eigenvalue of A corresponding to v.
What is the significance of an eigenvalue being zero in the context of linear algebra?
In linear algebra, an eigenvalue being zero indicates that the corresponding eigenvector is not stretched or compressed by the linear transformation. This means that the transformation collapses the vector onto a lower-dimensional subspace, which can provide important insights into the structure and behavior of the system being studied.
What does eigenvalues mean?
Well in linear algebra if given a vector space V,over a field F,and a linear function A:V->V (i.e for each x,y in V and a in F,A(ax+y)=aA(x)+A(y))then ''e" in F is said to be an eigenvalue of A ,if there is a nonzero vector v in V such that A(v)=ev.Now since every linear transformation can represented as a matrix so a more specific definition would be that if u have an NxN matrix "A" then "e" is an eigenvalue for "A" if there exists an N dimensional vector "v" such that Av=ev.Basically a matrix acts on an eigenvector(those vectors whose direction remains unchanged and only magnitude changes when a matrix acts on it) by multiplying its magnitude by a certain factor and this factor is called the eigenvalue of that eigenvector.
What is the eigen value?
This is the definition of eigenvectors and eigenvalues according to Wikipedia:Specifically, a non-zero column vector v is a (right) eigenvector of a matrix A if (and only if) there exists a number λ such that Av = λv. The number λ is called the eigenvalue corresponding to that vector. The set of all eigenvectors of a matrix, each paired with its corresponding eigenvalue, is called the eigensystemof that matrix
What is the significance of the maximal eigenvalue in the context of matrix analysis and how does it impact the overall properties of the matrix?
The maximal eigenvalue of a matrix is important in matrix analysis because it represents the largest scalar by which an eigenvector is scaled when multiplied by the matrix. This value can provide insights into the stability, convergence, and behavior of the matrix in various mathematical and scientific applications. Additionally, the maximal eigenvalue can impact the overall properties of the matrix, such as its spectral radius, condition number, and stability in numerical computations.
What is an eigenstate?
eigenstate(quantum mechanics) A dynamical state whose state vector (or wave function) is an eigenvector (or eigenfunction) of an operator corresponding to a specified physical quantity. energy state.Refer to: http://www.answers.com/eigenstate?cat=technology&gwp=11&method=3&ver=2.3.0.609
Show that eigen vectors corresponding to distinct eigen values of matrix A are linearly independent?
Let l1,...,lr be distinct eigenvalues of an nxn matrix A, and let v1,...,vr be the corresponding eigenvectors. This proof is by induction: The case r=1 is obvious since k1 is not the zero vector. Suppose that the theorem holds true for r=m-1, i.e. {k1,...,km-1} is linearly independent. This means c1k1+c2k2+...+cm-1km-1=0 (1) iff ci=0 for all i. Now suppose that a1k1+a2k2+...+am-1km-1+amkm=0 (2) If am is not equal to 0, then km=b1k1+b2k2+...+bm-1km-1 (3) where bi=-ai/am. Multiplying both sides of (3) by lmI-A (where I is the nxn identity matrix) and using the fact that Aki=liki, we have: 0=(l1-lm)b1k1+(l2-lm)b2k2+...+(lm-1-lm)bm-1km-1. By our induction hypothesis we have that (li-lm)bi=0 for each i. Thus by (3) km is the zero vector, which is a contradiction since it is an eigenvector. Thus it must be that am is zero. If am=0 in (2), then all of the ai=0 by the induction hypothesis. Thus {k1,...,km} is linearly independent. By induction this is true for all 1<=r<=n.
