Miscellaneous

1) ABS
Calculates the norm of a vectror
The norm of a vector [ a b c ] is definite as SQRT(a^2 + b^2 + c^2)

Example::
Find the norm of the vector [2 3 4]
level 1: [2 3 4]
[MTH][VECTR][ABS]

Result: 5.38516480713

2) DOT
Calculates the scalar product of two vectors.
The result is a number.

Example::
[2 3 4].[6 7 8]
level 2: [2 3 4]
level 1: [6 7 8]
[MTH][VECTR][DOT]

Result: 65

3) CROSS
Calculates the vectorial produc of two vectors.
The result is a vector.

Example::
[2 3 4] x [6 7 8]
level 2: [2 3 4]
level 1:[6 7 8]
[MTH][VECTR][CROSS]

Result: [-4 8 -4]

4)

V2
Convert numbers in levels 1 and 2 into a vector.

Example::
level 2: 9
level 1: 8

[MTH][VECTR][

V2]
Result: [9 8]

5)

V3
Convert numbers in levels 1, 2 and 3 into a vector.

Example::
level 3: 4
level 2: 5
level 1: 8
[MTH][VECTR][

V3]

Result: [4 5 8]

6) V

Convert a vector into stack numbers.

Example::
level 1:[2 6 1 ]
[MTH][VECTR][V

]

Result:
level 3: 2
level 2: 6
level 1: 1

In HP48/49 complexes numbers are represented between ( ).
as (real part, complex part)
Work with complexes numbers in HP48/49 is easy.
Below are listed the most useful functions.

1) RE
Returns the real part of a complex number

Example::
Find the real part of (123, 456)

Level 1: (123, 456)
Press [MTH][NXT][CMPL][RE]

Result: 123

2) IM
Returns the imaginary part of a complex number

Example::

Find the imaginary part of (123, 456)

Level 1: (123, 456)
Press [MTH][NXT][CMPL][IM]
Result: 456

3) ABS
Returns the norma of a complex number

Example::
Find the norm of the complex number (123, 456)

Level 1: (123, 456)
Press [MTH][NXT][CMPL][ABS]

Result: 472.297575687

4) ARG
Return the angle argument of a complex number

Example::
Find the angle argument of (123, 456)

Level 1: (123, 456)
Press [MTH][NXT][CMPL][ARG]

Result:
74.9044791558 (angle mode)
1.30732978576 (RAD mode)

5) CONJ
Return the conjugate of a complex number

Example::
Find the conjugate of (123, 456)

Level 1: (123, 456)
Press [MTH][NXT][CMPL][ARG]
Result: (123, -456)

1) RND
Rounds a number for a definite numbers of digits

Level 2: 1.8678987
Level 1:3
Press [MTH][REAL][RDN]

Result: 1.868

2) TRNC
Truncates a number to the set numbers of digits

Level 2: 1.8678987
Level 1:3
Press [MTH][REAL][TRNC]

Result: 1.867

3) MOD
Returns the rest of a division between two numbers

Example::

Level 2: 14
Level 1:3
Press [MTH][REAL][MOD]

Result: 2
Note: 8 / 3 = 4 and rest 2.

4) IP
Show the Integer Part of a number

Example::

Level 2: 1.8678987
Press [MTH][REAL][IP]

Result: 1

5) FP
Show the Fraction Part of a number

Example:

Level 2: 1.8678987
Press [MTH][REAL][FP]

Result:. 8678987

6) D

R
Converts from Degree to radians

Example:

Level 2: 45
Press [MTH][REAL][D

R]

Result: .785398163397

7) R

D
Converts from Radians to Degree

Example:

Level 2: .785398163397 Example:

Press [MTH][REAL][R

D]

Result: 45

8) CEIL
Returns the mayor integer closest to the number

Example:

Level 2: 1,45
Press [MTH][REAL][CEIL]

Result: 2

9) FLOOR
Returns the minor integer closest to the number

Example:

Level 2: 1,45
Press [MTH][REAL][FLOOR]

Result: 1

10) %
Returns the percentage

Example:

Level 2: 100
Level 1: 12,67
Press [MTH][REAL][%]

Result:12.67

Eigenvectors and Eigenvalues

1) EGV
The command EGV calculates the eigenvalues and the eigenvectors of a given matrix.

Example:

Calculates the eigenvalues and the eigenvectors of the matrix

Caracteristic Matrix

Resolution:
1- write the matrix in the HP48/49 as below:

Written the Matrix

and press [ENTER]

2- type EGV and press [ENTER]

It will show:

where the columns of the matrix are the eigenvectors associated
to the eigenvalues shown in the vector below the matrix.

In this Example:,
[1 0 0] is the eigenvector associated to 3
[1 1 0] is the eigenvector associated to 2
[3 3 1] is the eigenvector associated to 1

2) EGVL
The command EGVL calculate the eigenvector of a given matrix

Example:

Calculates the eigenvalues and the eigenvectors of the matrix

Caracteristic Matrix

Resolution:
1- write the matrix in the HP48/49 as below:

Written the Matrix

and press [ENTER]

2- type EGVL and press [ENTER]

It shows the vector [ 3 2 1]
where 3, 2 and 1 are the eigenvalues for the matrix.

Note:
These Examples was done with HP49 mode set RPN

HP48 is also able to calculate eigenvalues and eigenvectors,
but HP48 shows the eigenvector matrix in line,
and eigenvalues as a vector.

For the Examples of EGV above it shows something like,
[ [ 1 1 3 ] [ 0 1 3 ] [ 0 0 1] ]
[ 3 2 1].

Press [SWAP] to see it like.

[ 3 2 1]
[ [ 1 1 3 ]
[ 0 1 3 ]
[ 0 0 1 ] ]

Where the eigenvectors are shown as colums of the matrix,
and the eigenvalues as the vector [ 3 2 1].