# Subst; Subtmod; Svd; Svl - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Input/Output:
CHR, GOR, GXOR, NUM, POS, REPL, SIZE

## SUBST

CAS:
Substitute a value for a variable in an expression; the value can be numeric or an expression.

### SUBTMOD

CAS:
Perform a subtraction, modulo the current modulus.

### 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):
where diag(S) denotes the m × n diagonal matrix containing the singular values S.
Access:
Input/Output:
DIAG , MIN, SVL

### SVL

Type:
Command
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:
3-178 Full Command and Function Reference
Level 3/Argument 1
Level 2/Argument 2
[[ matrix ]]
1
[[ matrix ]]
1
[[ matrix ]]
1
[[ matrix ]]
1
"string
"
target
{ list
}
target
grob
target
grob
target
PICT
PICT
A U
-------------------------------------------------- -
min m n
FACTORIZATION SVD
MATRIX FACTORS SVD
Level 1/Argument 1
[[ matrix ]]
A
L
FACTORIZATION
SVL
L
MATRIX FACTORS
SVL
Level 1/Argument 3
n
n
startposition
{n
, n
}
n
row
column
n
{n
startposition
row
{n
, n
}
{n
row
column
row
n
n
startposition
n
n
startposition
{ #n
, #m
}
{ #n
1
1
( x
, y
)
( x
1
1
{ #n
, #m
}
{ #n
1
1
( x
, y
)
( x
1
1
diag S
V
A
(Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
Level 3/Item 1
[[ matrix ]]
U
(Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
Level 1/Item 1
[[ matrix ]]
endposition
[[ matrix ]]
endposition
,, n
}
[[ matrix ]]
column
,, n
}
[[ matrix ]]
column
"string
endposition
endposition
#m
}
2
2
, y
)
2
2
#m
}
2
2
, y
)
2
2
Level 2/Item 2
Level 1/Item 3
[[ matrix ]]
[ vector ]
V
2
2
2
2
"
result
{ list
}
result
grob
result
grob
result
grob
result
grob
result
S

49g+