Linear algebra, what does it mean to calculate the double root by the multiple number?

Linear algebra. The meaning of double root by multiple number is:

This is the category of eigenvalues and eigenvectors of sexual algebra. When finding the eigenvectors of the matrix that can be diagonalized, because each eigenvalue can correspond to a eigenvector, if the eigenvalue is a double root, if it is n double root, then it must correspond to n linearly independent eigenvectors, so when finding the eigenvector, the solution equation should be found according to the multiple number n of the heavy root.

Linear algebra is a branch of mathematics that studies vectors, vector spaces.

Or a system of linear equations for linear spaces, linear transformations, and finite dimensions. Vector space is an important topic in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis. Through analytic geometry, linear algebra can be concretely represented.

If it is a number of roots, it will be counted according to the number of roots. For example, 1 is a triple root, which means that there are 3 roots that are all 1.

For example, the root of 4-2 3+ 2=0 is 0,0,1,1, and its root can also be expressed as double root 0 and double root 1.

Equation f(x).

0 has a root, xa means that f(x) has a factor (x

a), so that polynomial division p(x) can be done

f(x)x-a) is still a polynomial. If p(x).

0 is still rooted in xa, then x=

a is the heavy root of the equation.

or let f1(x) be the derivative of f(x), if f1(x).

0 is also based on xa, which can also indicate x=

a is the double root of the equation f(x)=0.

Extended Information: The solution of a multivariate equation is the value of a set of unknowns. For example, x=2 and y=1 are a solution to the binary equation 2x-y=3. If several roots in the whole root of an equation are equal, then these roots are called double roots.

For example, the unary equation x3(x-1)2(x+3)=0, its root is x1=x2=x3=0, x4=x5=1, x6=-3, then "0" is its triple root, "1" is its double root, "-3" is not a double root, it can be called a single root, and generally only the double root problem is studied for integer equations.

The set of the whole solution of an equation is called the set of solutions of the equation, referred to as the solution set. If there is no solution to the equation, the solution set is an empty set. An equation without a solution is called a contradictory equation, so the set of solutions of a contradictory equation is an empty set.

If it is a number of roots, it will be counted according to the number of roots. For example, 1 is a triple root, which means that there are 3 roots that are all 1.

For example, the root of 4-2 3+ 2=0 is 0,0,1,1, and its root can also be expressed as double root 0 and double root 1.

The equation f(x) = 0 has a root x = a, then f(x) has a factor (x - a), so that polynomial division can be done p(x) = f(x) x-a) The result is still a polynomial. If p(x) =0 is still rooted in x = a, then x = a is the double root of the equation.

Or let f1(x) be the derivative of f(x), and if f1(x) =0 is also rooted by x =a, then it can also be shown that x= a is the double root of the equation f(x)=0.

If it is a number of roots, it will be counted according to the number of roots. For example, 1 is a triple root, which means that there are 3 roots that are all 1.

For example, the root of 4-2 3+ 2=0 is 0,0,1,1, and its root can also be expressed as double root 0 and double root 1.

The equation f(x) = 0 has a root x = a, then f(x) has a factor (x - a), so that polynomial division can be done p(x) = f(x) x-a) The result is still a polynomial. If p(x) =0 is still rooted in x = a, then x = a is the double root of the equation.

Or let f1(x) be the derivative of f(x), and if f1(x) =0 is also rooted by x =a, then it can also be shown that x= a is the double root of the equation f(x)=0.

Give an example of the difference between single root and double root:

General Formula Y''+py'+qy=pm(x)e (nx) As in the question, the eigenroots are 2 and 3, n=2, then 2 is a single root; If n = 3, then 3 is a single root.

For example, y''-4y'+4y=pm(x)e (nx) both of his eigenroots are 2, and if n=2, then 2 is a double root.

For example, (x-2) 3 takes zero when x is equal to 2, and x 2 is one root of the equation, because it is cubic and there are three roots in the multiplicity number.

For example, x is a triple root, which means that there are 3 roots that are x