HP 15C: Vector Operations
Calculators covered:
* HP 15C
* HP 15C Limited Edition
* HP 15C Collector's Edition
* Apps, Swiss Micros DM 15
HP 15C: Dot Product, Tensor Product, and Angle Between Vectors
Set vectors A and B as 3 x 1 vectors (3 rows, 1 column)
3 ENTER 1 dim A
3 ENTER 1 dim B
Dot Product (LBL D)
Dot product: A ⋅ B = A^T B
The result is a single number.
Code:
001 : 42,21,14 : LBL D
002 : 45,16,11 : RCL MATRIX A
003 : 42,16, 4 : MATRIX 4
004 : 45, 16, 12 : RCL MATRIX B
005 : 42, 26, 13 : RESULT C
006 : 20 : ×
007 : 45,16,11 : RCL MATRIX A
008 : 42,16, 4 : MATRIX 4
009 : 45,13 : RCL C
010 : 43,32 : RTN
Tensor Product (LBL E)
Tensor product: A ⊗ B = A B^T
The result is a 3 x 3 matrix
Code:
011 : 42,21,15 : LBL E
012 : 45,16,11 : RCL MATRIX A
013 : 45,16,12 : RCL MATRIX B
014 : 42,16, 4 : MATRIX 4
015 : 42,26,13 : RESULT C
016 : 20 : ×
017 : 45,16,12 : RCL MATRIX B
018 : 41,16, 4 : MATRIX 4
019 : 42,16, 1 : MATRIX 1
020 : 45,16,13 : RCL MATRIX C
021 : 43, 32 : RTN
Angle Between Vectors (LBL 0)
θ = arccos( (A ⋅ B) ÷ (||A|| ||B||) )
Code:
022 : 42,21, 0 : LBL 0
023 : 32,14 : GSB D
024 : 45,16,11 : RCL MATRIX A
025 : 42,16, 8 : MATRIX 8
026 : 45,16,12 : RCL MATRIX B
027 : 42,16, 8 : MATRIX 8
028 : 20 : ×
029 : 10 : ÷
030 : 43,24 : COS^-1
031 : 43,32 : RTN
Notes:
MATRIX 4: Transposes a matrix, which it is stored in the original matrix slot.
MATRIX 8: The 2-norm of a matrix. It is calculated by taking a square root of the sum of the square of each element. √(Σ( A_r,c ^ 2, r = 1 to n and c = 1 to m))
For the dot and tensor products, I transpose the appropriate matrix back to the 3 x 1 form after the calculation.
Example
A = [ [ 4 ], [ 5 ], [ -2 ] ]
B = [ [ -3 ], [ 9 ], [ 8 ] ]
Dot Product: GTO D R/S
Result: 17
Tensor Product: GTO E R/S
Result:
[ [ -12, 36, 32 ], [ -15, 45, 40 ], [ 6, -18, -16 ] ]
Angle Between Vectors: GTO 0 R/S
Result: 78.2166°
Eddie
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