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Basic Linear Algebra Summary Sheet

by Dan Sunday

 

 

Notation,  Definitions and Basic Equations

 

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

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© Copyright 2012 Dan Sunday, 2001 softSurfer