dy/dx - = 1 - y,y(0) = 0 is an example of

[cyberian]

Let A be an n × n matrix. Then λ = 0 is an eigenvalue of A if and only if there exists a non-zero vector v ∈ Rn such that Av = λv = 0. In other words, 0 is an eigenvalue of A if and only if the vector equation Ax = 0 has a non-zero solution x ∈ Rn.

[cyberian]

an eigenvector v is said to be normalized if the coordinate of largest magnitude is equal to aero?

[cyberian]

Two similar matrices have the same eigenvalues, even though they will usually have different eigenvectors. Said more precisely, if B = Ai’AJ. I and x is an eigenvector of A, then M’x is an eigenvector of B = M’AM. So, A1’x is an eigenvector for B, with eigenvalue ).

[cyberian]

b) The eigenvalues of a real symmetric matrix need not be positive. They can be positive, negative, or even zero, depending on the elements and the specific structure of the matrix.

[cyberian]

Jacobian Method in Matrix Form
Let the n system of linear equations be Ax = b. Let us decompose matrix A into a diagonal component D and remainder R such that A = D + R. Iteratively the solution will be obtained using the below equation.

[cyberian]

for a function; y=f(x), if y0, y1 are 2,3

[cyberian]

how many eigenvalues will exit corresponding to the function exp(ax)

[cyberian]