[선형대수] Sage - Power method, Various Eigenvalues, Complex Eigenvalues, Linear Transformation

소개글

A. Power method for estimating a strictly dominant eigenvalue and its eigenvector
1. Let
2. Repeat the following UNTIL
a. Let be the entry of whose absolute value is largest,
and let .
b. In the new line, print up to five decimal places.
c. Compute .
d.
3. Plot the points in a figure.

B. Various Eigenvalues
1. Let Note that all of them have the same eigenvectors
2. Let
3. For i=1, 2, 3
a. For j=1, 2, ..., 8, repeat the following:
- Let
- Compute by the rule .
b. Plot all points in a figure.

C. Complex Eigenvalues
1. Let Let
2. Compute and print the two eigenvalues of A.
3. By the rule , compute .
4. Plot all the points in a figure.

D. Linear Transformation
1. Let
Let be the i-th column of H.
2. Draw the house represented by H, as follows:
- Draw black dots at 12 points .
- Draw line segments between every and between and .
3.Let
.
With , run STEP 2, one by one.

컴파일 실행환경

Sage

압축파일 내 파일목록

hw3.hwp
20052710.txt

참고 자료

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