Logo_iSurf_org

Subscribe
to eAlerts
for Geom Site
Updates

CLICK HERE

 
Basic Linear Algebra Summary Sheet

by Dan Sunday

 

 

 

Notation

Scalars

lower case italic

 a,b...x,y...

Points

UPPER CASE ITALIC

 P, Q, R, V, ...
P=(p1,p2,...pn)=(pi)

Vectors

lower case bold

 a, b, ..., u, v, w, ...
v=(v1...vn)=(vi)

Geometric Objects

UPPER CASE BOLD

L, R, S, T, ..., P, ...
DELTA, OMEGA, PSI, THETA-cap-bold, ..., DELTA-P0P1P2, ...

Functions

Regular font

A(OMEGA), ..., f(x), ...

 

Font of the result

P(t)=(x(t),y(t)), v(x,y), ...

Operation

Definition

Basic Equations

Point Difference

v=Q-P=(qi-pi)

 

Vector Addition

vect_add_define

vect_add_assoc
vect_add_commute

Point+Vector Addition

P+v=(pi+vi)

vect_add_point_assoc

Scalar Multiplication

vect_scalar_mult_define

vect_scalar_assoc
vect_scalar_distrib
vect_add_distrib

Point Affine Sum

affine-sum-aiPi-define-short

affine-sum-P+v=...
M=(P0+P1)-half
P=(1-t)P0+tP1
P=(1-s-t)P0+sP1+tP2

Vector Length

vect_len_define-short

vect_len_assoc
abs-(v+w).le.abs-v+abs-w
vect_Cosine-Law-short

Dot Product

dot_prod-define

dot-scalar-assoc
dot_prod-commute
dot-distrib-left
dot-abs-(v_dot_w).le.abs-v_abs-w

dot-v.w=abs-vw-cos
dot-v.w=cos-long
dot_prod_angle_inequal-short

2D Perp Operator

perp_op_define

perp_op_normal
perp_op_length
perp_op_scalar-assoc
perp_op_linear
perp_op_antipotent

2D Perp Product

perp_prod_define-short

        where  determ_abcd=ad-bc

perp_prod_nilpotent
perp_prod_scalar-assoc
perp_prod_antisymmetry
perp_prod_distrib-left
perp_dot_Lagrange-ID

perp-v.w=abs-vw-sin
perp-v.w=sin-long
Area_P0P1P2=perp-10-20-half
perp_prod_angle_inequal-short

3D Cross Product

cross_prod_define

cross_prod_nilpotent
cross_prod_scalar-assoc
cross_prod_antisym
cross_prod_add-distrib-left
cross_prod_nomal
cross_dot_Lagrange-ID1

cross_prod_left_assoc_uvw
cross_prod_right_assoc_uvw
dot_cross_assoc
cross_dot_Lagrange-ID2
cross_prod_Jacobi-ID

vxw-abs=vw_sin
Area_P0P1P2=cross-v-w-half-short

3D Triple Product

triple_prod_define

triple_prod_permute
triple_prod_antisym
triple_prod_triple-cross
Vol_uvw=triple-uvw
Vol_P0P1P2P3=triple-uvw-sixth-short

Previous: Vector Products
NavLeft

 

© Copyright 2012 Dan Sunday, 2001 softSurfer