HP35S  Inverse of a 3x3 matrix (but also determinant, cross product, etc.)

09282023, 12:12 PM
(This post was last modified: 09282023 12:16 PM by Roberto Volpi.)
Post: #1




HP35S  Inverse of a 3x3 matrix (but also determinant, cross product, etc.)
Hi all,
the following is an improvement of an already submitted program of mine: https://www.hpmuseum.org/forum/thread18512.html The purpose is to have in just 1 place a quick tool to find, in a 3x3 matrix: Determinant Inverse matrix Cross product Angle between two 3D vectors. Maybe one day also Eigenvectors and Eigenvalues... M001 LBL M M002 SF1 M003 XEQ X001 M004 STO P M005 R down M006 STO C M007 R down M008 STO B M009 R down M010 STO A M011 SF 10 M012 (equ) 2DN VECTOR Q M013 CF 10 M014 XEQ X001 M015 STO Q M016 R down M017 STO F M018 R down M019 STO E M020 R down M021 STO T M022 (eqn) [BxFCxE, CxTAxF, AxEBxT] M023 STO X M024 FS 1? M025 GTO M028 M026 VIEW X M027 GTO M058 M028 SF 10 M029 (eqn) 3RD VECTOR R M030 CF 10 M031 XEQ X001 M032 STO R M033 R down M034 STO N M035 R down M036 STO H M037 R down M038 STO G M039 R down M040 RCLxX M041 STO D M042 CF 1 M043 VIEW D M044 RCL+C M045 (eqn) [ExNFxH, CxHBxN, BxFExC] M046 STO K M047 (eqn) [FxGTxN, AxNCxG, TxCAxF] M048 STO L M049 (eqn) [TxHGxE, BxGAxH, AxEBxT] M050 STO M M051 RCL D M052 STO/K M053 STO/L M054 STO/M M055 RCL K M056 RCL L M057 RCL M M058 RTN M059 RCL X M060 ABS M061 RCL P M062 RCLxQ M063 / M064 ATAN M065 >DEG M066 STO Y M067 VIEW Y M068 RTN I have separated the following routine, as it may be used as an additional function, to put values on stacks z, y and x into a 3d vector X001 LBL X X002 (eqn) [RegZ, RegY, RegX] X003 RTN  INSTRUCTIONS:  DETERMINANT + INVERSE MATRIX enter 1st row, an entry per stack XEQ M enter 2nd row, an entry per stack R/S enter 3rd row, an entry per stack R/S HP35S: D= determinant value R/S HP35S: inverse matrix arranged this way: stack t:determinant stack z: 1st row stack y: 2nd row stack x: 3rd row CROSS PRODUCT + ANGLE (1st & 2nd row vector) enter 1st vector, an entry per stack XEQM003 enter 2nd vector, an entry per stack R/S HP35S: X= cross product value R/S HP35S: Y= angle in DEG CROSS PRODUCT + ANGLE of first 2 rows after finding determinant and inverse matrix: RCL X to recall cross product XEQ M058 to find the angle in DEG DETERMINANT & INVERSE MATRIX after finding cross product (and/or angle) XEQ M028 Enter 3rd row vector, an entry per stack R/S HP35S: determinant and inverse matrix arranged this way: stack t:determinant stack z: 1st row stack y: 2nd row stack x: 3rd row Enjoy! Put a calculator into your life! 

09282023, 08:52 PM
Post: #2




RE: HP35S  Inverse of a 3x3 matrix (but also determinant, cross product, etc.)
Please, could you please include one example for each calculation type. It will be very useful for everybody to check the correct program typing keys and procedure. Thank you in advance for your effort and sharing this valuable program. Pedro


09302023, 09:35 AM
Post: #3




RE: HP35S  Inverse of a 3x3 matrix (but also determinant, cross product, etc.)
Dear Pedro
here quick examples as requested: 1) Determinant and inverse of following matrix: 1, 2, 3 4, 5, 6 7, 8, 9 Press: 1 ENTER 2 ENTER 3 XEQ M ENTER The calculator will ask for the 2nd row vector Press: 4 ENTER 5 ENTER 6 R/S The calculator will ask for the 3rd row vector Press: 7 ENTER 8 ENTER 9 R/S The calculator will display "D=54" which is the determinant Press: R/S The calculator will display 2nd and 3rd row vectors of inverse matrix in 3D vector form. Stack values will be as follows, with entries in FDISP for easier readability: Stack t: 54 (which is the determinant value) Stack z: [ 1+13/18, 7/9, 1/18 ] (1st row vector of inverse matrix) Stack y: [ 1+4/9, 5/9, 1/9 ] (2nd row vector of inverse matrix) Stack x: [1/18, 1/9, 1/18] (3rd row vector of inverse matrix) 2) Cross product and angle of first 2 row vectors already inputed Cross vector: RCL X, which gives [ 3, 6, 3 ] Angle: Press XEQ M058, which gives Y=12.9331... as DEG 3) Cross product and angle of 2 3D vectors: [ 3, 2, 1 ] [ 7, 5, 2] Press: 3 ENTER 2 ENTER 1 XEQ M003 The calculator will ask for the 2nd vector Press: 7 ENTER 5 ENTER 2 R/S The calculator will display X= [ 9, 13, 1 ], which is the cross product Press R/S, and the calculator will display Y=28.6482..., which is the angle in DEG mode 4) Determinant and inverse matrix made after adding a 3rd row vector to former example: 3rd row vector: [ 1, 2, 6 ] Press: XEQ M028 1 ENTER 2 ENTER 6 R/S The calculator will display D=11, which is the determinant Press R/S The calculator will display 2nd and 3rd row vectors of inverse matrix in 3D vector form. Stack values will be as follows, with entries in FDISP for easier readability: Stack t: 1 (which is the determinant value) Stack z: [ 2+4/11, 1+3/11, 9/11 ] (1st row vector of inverse matrix) Stack y: [ 3+7/11, 1+8/11, 1+2/11 ] (2nd row vector of inverse matrix) Stack x: [ 9/11, 4/11, 1/11] (3rd row vector of inverse matrix) Hope no typo is ruining these examples... Put a calculator into your life! 

09302023, 03:22 PM
Post: #4




RE: HP35S  Inverse of a 3x3 matrix (but also determinant, cross product, etc.)
This is perfect, TYVM. Now I feel confident to use your program. Very clear informaciĆ³n to test the PGRM. Pedro


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