Input: Level 2/Argument 1: The object or number to be subtracted from.

Level 1/Argument 2: The object or number to subtract.

Output: The result of the subtraction, modulo the current modulus.

Flags: Exact mode must be set (flag –105 clear).

Numeric mode must not be set (flag –3 clear).

Radians mode must be set (flag –17 set).

SVD

Type: Command

Description: Singular Value Decomposition Command: Returns the singular value decomposition of an m × n matrix.

SVD decomposes A into 2 matrices and a vector. U is an m × m orthogonal matrix, V is an n × n orthogonal matrix, and S is a real vector, such that A = U × diag(S) × V . S has length MIN(m,n) and contains the singular values of A in nonincreasing order. The matrix diag(S) is an m×n diagonal matrix containing the singular values S.

The computed results should minimize (within computational precision):

A– U ⋅ diag(S) ⋅ V

--------------------------------------------------

min(m, n) ⋅ A

where diag(S) denotes the m × n diagonal matrix containing the singular values S.

Access:

!Ø FACTORIZATION SVD

 

(Ø is the left-shift of the 5key).

 

!´MATRIX FACTORS SVD

 

( ´is the left-shift of the Pkey).

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

Level 3/Item 1

Level 2/Item 2

Level 1/Item 3

 

 

 

 

 

 

 

 

 

[[ matrix ]]A

→

[[ matrix ]]U

[[ matrix ]]V

[ vector ]S

 

 

 

 

 

 

 

See also:

DIAG→, MIN, SVL

 

 

 

 

 

 

 

 

 

 

 

SVL

Command

 

 

 

 

Type:

 

 

 

 

Description:

Singular Values Command: Returns the singular values of an m × n matrix.

 

 

SLV returns a real vector that contains the singular values of an m × n matrix in non-increasing

 

order. The vector has length MIN(m,n).

 

 

 

Access:

!Ø FACTORIZATION LSVL (Ø is the left-shift of the 5key).

 

 

!´MATRIX FACTORS LSVL ( ´is the left-shift of the Pkey).

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

Level 1/Item 1

 

 

 

 

 

 

 

[[ matrix ]]

→

[ vector ]

See also:

MIN, SVD

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SWAP

RPL Command

 

 

 

 

Type:

 

 

 

 

Description:

Swap Objects Command: Swaps the position of the two inputs.

 

Access:

!°STACK SWAP

 

( °is the left-shift of the Nkey).

™in RPN mode executes SWAP when no command line is present.

Input/Output:

Level 2

Level 1

 

Level 2

Level 1

 

 

 

 

 

obj1

obj2

→

obj2

obj1

 

 

 

 

 

3-244 Full Command and Function Reference