MATRIX("PENTADIAGONAL",order)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order}
is the size of the Pentadiagonal matrix.
Description
- This function gives the pentadiagonal matrix of order 3.
- A pentadiagonal matrix is a matrix that is nearly diagonal.
- So it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it.
- The form of pentadiagonal matrix is:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\begin{pmatrix} c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\ b_1 & c_2 & d_2 & e_2 & \ddots &\cdots & \vdots \\ a_1 & b_2 & \cdots & \ddots & \ddots & \ddots & \vdots \\ 0 & a_2 & \cdots & \ddots & \ddots & e_{n-3} & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\ \vdots &\cdots& \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\ 0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n \end{pmatrix}}
.
- When n is the size of the matrix, a pentadiagonal matrix has atmost 5n-6 nonzero entries.
- Here MATIRX("pentadiagonal") is showing the penta diagonal matrix of order 3 with the integer numbers.
- Also in Calci users can get a deimal values with positive and negative numbers.
- The syntax is to get the decimal penta diagonal matrix is MATRIX("pentadiagonal:negative") and MATRIX(pentadiagonal:positive")
Examples
- 1.MATRIX("pentadiagonal") =22
- 2.MATRIX("pentadiagonal",3)
| -58 |
15 |
-4
|
| -54 |
55 |
-75
|
| 21 |
-25 |
-64
|
- 3.MATRIX("pentadiagonal",6)
| 54 |
-56 |
-28 |
0 |
0 |
0
|
| 62 |
-96 |
-82 |
-49 |
0 |
0
|
| 15 |
23 |
20 |
30 |
94 |
0
|
| 0 |
80 |
95 |
76 |
-82 |
66
|
| 0 |
0 |
-60 |
-27 |
-82 |
-87
|
| 0 |
0 |
0 |
-43 |
19 |
89
|
- 4.MATRIX("pentadiagonal:negative",4)
| -59.92012487258762 |
-79.75753229111433 |
-20.13208125717938 |
0
|
| -47.0609312877059 |
-7.832704461179674 |
-29.973211092874408 |
-12.44902245234698
|
| -47.85296192858368 |
-67.0970072504133 |
-53.094227402471006 |
-84.4662182033062
|
| 0 |
-12.941046571359038 |
-31.090207281522453 |
-52.342877350747585
|
- 5.MATRIX("pentadiagonal:positive",5)
| 86.68749532662332 |
69.28418821189553 |
15.4073191806674 |
0 |
0
|
| 35.21442376077175 |
31.06112303212285 |
35.75007226318121 |
77.74382838979363 |
0
|
| 24.096227367408574 |
42.69053868483752 |
98.5696179093793 |
5.866385693661869 |
81.69623236171901
|
| 0 |
80.96880922093987 |
67.79956801328808 |
45.05093654152006 |
71.03362120687962
|
| 0 |
0 |
32.176876766607165 |
47.92787255719304 |
48.10425683390349
|
See Also
References