HP 15c Manual

 Section 12: Calculating with Matrices 141 
 
Matrix inversion, for example, can be performed on an 8×8 matrix with real 
elements (or on a 4×4 matrix with complex elements, as described later*). 
To conserve memory, all matrices are initially dimensioned as 0×0. When a 
matrix  is  dimensioned  or  redimensioned,  the  proper  number  of  registers  is 
automatically  allocated  in  memory.  You  may  have  to  increase  the  number 
of  registers  allocated  to  matrix  memory  before  dimensioning  a...

142 Section 12: Calculating with Matrices 
 
Example: Dimension matrix A to be a 2×3 matrix. 
Keystrokes Display  
2 v 2.0000 Keys number of rows into  
Y-register. 
3 3 Keys number of columns into X-
register. 
´mA 3.0000 Dimensions matrix A to be 2×3. 
Displaying Matrix Dimensions 
There are two ways you can display the dimensions of a matrix: 
 Press l > followed by the letter key specifying the 
matrix. The calculator displays the name of the matrix at the left, 
and the number of rows followed by...

 Section 12: Calculating with Matrices 143 
 
If  you  redimension a  matrix  to  a  larger  size,  elements  with  the  value  0  are 
added  at  the  end  as  required  by  the  new  dimensions.  For  example,  if  the 
same 2×3 matrix is re dimensioned, to 2×4, then 
 
When  you  have  finished  calculating  with  matrices,  youll  probably  want  to 
redimension  all  five  matrices  to 0×0,  so  that  the  registers  used  for  storing 
their  elements  will  be  available  for  program  lines  or...

144 Section 12: Calculating with Matrices 
 
To store or recall sequential elements of a matrix: 
1. Be sure the matrix is properly dimensioned. 
2. Press ´ >1.  This  stores  1  in  both  storage  registers  R0 and 
R1, so that elements will be accessed starting at row 1, column 1. 
3. Activate  User  mode  by  pressing ´ U.  With  the  calculator  in 
User  mode,  after  each  element  is  stored  or  recalled  the  row  number 
in R0 or the column number in R1 is automatically incremented by 1, 
as...

 Section 12: Calculating with Matrices 145 
 
 
Keystrokes Display  
´ > 1  Sets beginning row and column 
numbers in R0 and R1 to 1. 
(Display shows the previous 
result.) 
´ U  Activates User mode. 
1 O A A    1,1 Row 1, column 1 of A. 
(Displayed momentarily while 
A key held down.) 
 1.0000 Value of a11. 
2 O A 2.0000 Value of a12. 
3 O A 3.0000 Value of a13. 
4 O A 4.0000 Value of a21. 
5 O A 5.0000 Value of a22. 
6 O A 6.0000 Value of a23. 
lA A    1,1 Recalls element in row 1, 
column l. (R0 and...

146 Section 12: Calculating with Matrices 
 
Using  R0 and R1. To  access  a  particular  matrix  element,  store  its  row 
number  in  R0 and  its  column  number  in  R1.  These  numbers  wont  change 
automatically (unless the calculator is in User mode). 
 To  recall  the  element  value  (after  storing  the  row and  column 
numbers),  press l followed  by  the  letter  key  specifying  the 
matrix. 
 To  store  a  value  in  that  element  (after  storing  the  row  and  column 
numbers),...

 Section 12: Calculating with Matrices 147 
 
Example: Recall  the  element  in  row  2,  column  1  of  matrix A from  the 
previous example. Use the stack registers. 
Keystrokes Display  
2 v 1 1 Enters row number into Y-
register and column number into 
X-register. 
l | A 4.0000 Value of a21. 
Storing a Number in All Elements of a Matrix 
To  store  a  number  in  all  elements  of  a  matrix,  simply  key  that  number  into 
the  display, then press O> followed by the letter key specifying 
the...

148 Section 12: Calculating with Matrices 
 
operate  on  the  matrices  whose  descriptors  are  placed  in  the  X-register  and 
(for some operations) the Y-register. 
Two  matrix  operations – calculating  a  determinant  and  solving  the  matrix 
equation AX = B – involve  calculating  an LU decomposition  (also  known 
as  an LU  factorization)  of  the  matrix  specified  in  the  X-register.* A  matrix 
that is an LU decomposition is signified by two dashes following the matrix 
name  in  the...

 Section 12: Calculating with Matrices 149 
 
While the key used for any matrix operation that stores a result in the result 
matrix  is  held  down,  the  descriptor  of  the  result  matrix  is  displayed.  If  the 
key  is  released  within  about  3  seconds,  the  operation  is  performed,  and  the 
descriptor  of  the  result  matrix  is  placed  in  the  X-register.  If  the  key  is  held 
down  longer,  the  operation  is  not  performed  and  the  calculator  displays 
null. 
Copying a Matrix...

150 Section 12: Calculating with Matrices 
 
One-Matrix Operations: 
Sign Change, Inverse, Transpose, Norms, Determinant 
Keystroke(s) Result in  
X-register 
Effect on Matrix 
Specified in  
X-register 
Effect on Result 
Matrix 
“ No change. Changes sign of 
all elements. 
None. ‡ 
∕ 
(´∕ in 
User Mode) 
Descriptor of 
result matrix. 
None. ‡ Inverse of 
specified matrix. 
§ 
´> 4 Descriptor of 
transpose. 
Replaced by 
transpose. 
None. ‡ 
´> 7 Row norm of 
specified 
matrix.* 
None. None. 
´> 8...