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EvLer
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I need a bit of explanation on the conditions under which there is an eigenvalue that is equal to zero and what it's "physical" meaning.
Thanks in advance.
Thanks in advance.
EvLer said:um, actually no physics, just math class, I was trying to get a better understanding of eigenvalues and how those two say something about each other, matrices and eigenvalues/vectors that is...
ZioX said:By definition, an eigenvalue c will be a solution to det(A-cI)=0. If c=0, then det(A)=0.
EvLer said:um, actually no physics, just math class, I was trying to get a better understanding of eigenvalues and how those two say something about each other, matrices and eigenvalues/vectors that is...
JasonRox said:Really?
Let A = cI, then det(A-cI)=0, but det(A) is not equal to 0. How did you deduce that conclusion?
ZioX said:By definition, an eigenvalue c will be a solution to det(A-cI)=0. If c=0, then det(A)=0.
JasonRox said:Really?
Let A = cI, then det(A-cI)=0, but det(A) is not equal to 0. How did you deduce that conclusion?
The eigenvalue of 0 is a special value that can be obtained when solving for the eigenvalues of a matrix. It is important in physics because it can indicate the presence of a conserved quantity or symmetry in a physical system.
The eigenvalue of 0 can indicate degeneracy in a system, meaning that there are multiple eigenstates with the same energy. This is commonly seen in quantum systems with symmetries, such as the hydrogen atom.
An eigenvalue of 0 can have various physical interpretations depending on the specific system. In some cases, it can represent a conserved quantity, such as the total angular momentum in a spherically symmetric system. In other cases, it can indicate a symmetry or degeneracy in the system.
No, the eigenvalue of 0 is always a real number. This is because it is a special case that occurs when solving for the eigenvalues of a matrix, and any complex or negative eigenvalues would not satisfy the characteristic equation of the matrix.
The eigenvalue of 0, along with the corresponding eigenvector, can provide insight into the behavior and properties of a physical system. It can help identify conserved quantities, symmetries, and degeneracies, which can aid in the understanding and analysis of the system.