# How do you solve the Cayley Hamilton theorem?

## How do you solve the Cayley Hamilton theorem?

The Cayley Hamilton Theorem states that all real and complex square matrices will satisfy their own characteristic polynomial equation….Cayley Hamilton Theorem.

1. What is Cayley Hamilton Theorem?
2. Cayley Hamilton Theorem Formula
3. Cayley Hamilton Theorem Proof
4. Cayley Hamilton Theorem Applications

What is Cayley Hamilton method?

In linear algebra, the Cayley–Hamilton theorem (termed after the mathematicians Arthur Cayley and William Rowan Hamilton) says that every square matrix over a commutative ring (for instance the real or complex field) satisfies its own characteristic equation.

Why do we use Cayley-Hamilton theorem?

The Cayley-Hamilton theorem is usually presented in standard undergraduate courses in linear algebra as an important result. Recall that it says that any square matrix is a “root” of its own characteristic polynomial.

### How do you find the 100 Cayley-Hamilton theorem?

Use the Cayley-Hamilton Theorem to Compute the Power A100

1. (b) Let.
2. Note that the product of all eigenvalues of A is the determinant of A.
3. To use the Cayley-Hamilton theorem, we first need to determine the characteristic polynomial p(t)=det(A−tI) of A.
4. Then the Cayley-Hamilton theorem yields that.

How do you find the eigen vector on a calculator?

How to Use the Eigenvalue Calculator?

1. Step 1: Enter the 2×2 or 3×3 matrix elements in the respective input field.
2. Step 2: Now click the button “Calculate Eigenvalues ” or “Calculate Eigenvectors” to get the result.
3. Step 3: Finally, the eigenvalues or eigenvectors of the matrix will be displayed in the new window.

How do you find a 50 matrix?

First note that 50=32+16+2. Let A=(2021). A32=(6553601310701)(6553601310701)=(4294967296085899345901). Finally A50=(4294967296085899345901)(6553601310701)(4061).

#### How do you calculate eigenvalues?

Steps to Find Eigenvalues of a Matrix

1. Step 1: Make sure the given matrix A is a square matrix.
2. Step 2: Estimate the matrix.
3. Step 3: Find the determinant of matrix.
4. Step 4: From the equation thus obtained, calculate all the possible values of.
5. Example 2: Find the eigenvalues of.
6. Solution –

How do you prove the Cayley-Hamilton theorem?

The proof of Cayley-Hamilton therefore proceeds by approximating arbitrary matrices with diagonalizable matrices (this will be possible to do when entries of the matrix are complex, exploiting the fundamental theorem of algebra ). To do this, first one needs a criterion for diagonalizability of a matrix: M M is diagonalizable.

How do you find the value of a determinant in Cayley-Hamilton theorem?

First, in Cayley–Hamilton theorem, p ( A) is an n×n matrix. However, the right hand side of the above equation is the value of a determinant, which is a scalar. So they cannot be equated unless n = 1 (i.e. A is just a scalar). Second, in the expression .

## What is the Cayley-Hamilton theorem for a 3×3 matrix?

So, for a 3×3 matrix A, the statement of the Cayley–Hamilton theorem can also be written as where the right-hand side designates a 3×3 matrix with all entries reduced to zero. Likewise, this determinant in the n = 3 case, is now