Applied Maths Al Cheat sheet (214)
ors
, a e
(4)
q =
q = (a
product
D
& :
1 =
a , b, +
a b2 +
abs =
abcost a b = 0
torthogonal vectors
T
ba =
a b =
a xb axb =
0 >
-
norm to a adb
Norm
-
Hall = -
a a 9 2
+ +
=
a
a = * (a) = a (wit vector)
InR
-parameter
E =
p +
ta tz(- - 4),
Picto a *
↓
anchor
orientation
Vector
·. atto . . ,
(f ↓
T
1 =
p + ta
-
-
from
origin
in R
Pres cross product :
Normal
to plane
Pr es
through origin A =
Ax
parametric :
E =
q+ S& +
th =
2bs-a, bu) I
(a -
(a ,
b -A b
, , ,)f (a b2 -a b) T
,
Corthogonal)
Norm
1 .
1 =
0
vectors Acosrle
givenTe Angle
between
-bl
2
1) A =
a + b2-ZaBrosO
shift plane not
though origin
>
-
to position- replace I with -R
=> a tab +asby ,
= abos
Af
e ↓
e
scalar
=
] q .
b = abcost
, Matrics
- -
square matrices (nxn)
>
-
Matrix add is
LES :
·
(AT)" =
A
+
·
(A + B) =
At + BT
A+B =
B + A commutative
T
(B + C) (A + B) + (B) BA
·
A+ associative
=
= C
-
Face
>
-
scalar mult is :
↓A = AX commutative
-r(A) = a + A2 +
A33
-
>
-
Matrix melt is not commutative
(sum of diagonal)
of 2x2 :
Inverse
CABC=(ABILAme
e
(A + B) C
distributivig
=
AC + BL
Isame order At =ab [
1
(AT) (AT)
-
·
=
Permutation Matrix
>
-
Inverse matrix after row swapped metry
I
issameri, it stStab e
↳ swaps rows
pro-melt
>
-
Pt PT
I
=
i
Elementary row-op Matrix
e
Es ,
Marrie
Triangula
=
upper
:
-
matrices
Diagonal
I BoI (2008) Damon of = of t
L O
De D =
D"
premut by diagmai-scales theto
ens
-
-
ors
, a e
(4)
q =
q = (a
product
D
& :
1 =
a , b, +
a b2 +
abs =
abcost a b = 0
torthogonal vectors
T
ba =
a b =
a xb axb =
0 >
-
norm to a adb
Norm
-
Hall = -
a a 9 2
+ +
=
a
a = * (a) = a (wit vector)
InR
-parameter
E =
p +
ta tz(- - 4),
Picto a *
↓
anchor
orientation
Vector
·. atto . . ,
(f ↓
T
1 =
p + ta
-
-
from
origin
in R
Pres cross product :
Normal
to plane
Pr es
through origin A =
Ax
parametric :
E =
q+ S& +
th =
2bs-a, bu) I
(a -
(a ,
b -A b
, , ,)f (a b2 -a b) T
,
Corthogonal)
Norm
1 .
1 =
0
vectors Acosrle
givenTe Angle
between
-bl
2
1) A =
a + b2-ZaBrosO
shift plane not
though origin
>
-
to position- replace I with -R
=> a tab +asby ,
= abos
Af
e ↓
e
scalar
=
] q .
b = abcost
, Matrics
- -
square matrices (nxn)
>
-
Matrix add is
LES :
·
(AT)" =
A
+
·
(A + B) =
At + BT
A+B =
B + A commutative
T
(B + C) (A + B) + (B) BA
·
A+ associative
=
= C
-
Face
>
-
scalar mult is :
↓A = AX commutative
-r(A) = a + A2 +
A33
-
>
-
Matrix melt is not commutative
(sum of diagonal)
of 2x2 :
Inverse
CABC=(ABILAme
e
(A + B) C
distributivig
=
AC + BL
Isame order At =ab [
1
(AT) (AT)
-
·
=
Permutation Matrix
>
-
Inverse matrix after row swapped metry
I
issameri, it stStab e
↳ swaps rows
pro-melt
>
-
Pt PT
I
=
i
Elementary row-op Matrix
e
Es ,
Marrie
Triangula
=
upper
:
-
matrices
Diagonal
I BoI (2008) Damon of = of t
L O
De D =
D"
premut by diagmai-scales theto
ens
-
-
