 dot product
: The dot product or scalar product between
two vectors is formed by matching up corresponding coordinates,
multiplying then adding. For example
(1,2,3) · (4,5,6) = 1(4) + 2(5) + 3(6) = 32.
In MATLAB this could be done with the following commands:
>> a = [1,2,3]; b = [4,5,6]; % define two vectors
>> dot(a,b) % returns 32
Which uses the
dot
command. Alternatively we could have used
matrix
multiplication
>> a * b' % using matrix multiplication
 cross product
: The cross product between two
threedimensional vectors u and v is a vector with
direction given by the righthand rule and magnitude given by
uvsinq. In MATLAB it is found with the
cross
command
>> u = [1,2,3]; v = [4,5,6]; % two vectors
>> w = cross(u,v) % the cross product
ans = 3 6 3
>> dot(u,w) % cross product is orthogonal to u and v
ans = 0
 scalar
: In Linear Algebra, a scalar is a name for a real
number.
 matrices
and a matrix
: In Linear Algebra a
matrix is a n × m tabular array of numbers with n rows and
m columns. Matrices are quite useful for things such as keeping
track of systems of equations, keeping track of connections between
nodes on a graph, or even representing operations of a robot arm
such as rotations. In MATLAB we can enter a matrix quite easily. For
example this enters in a 2 by 3 matrix
>> [1, 2, 3; 4, 5, 6] % the matrix [1 2 3]
% [4 5 6]
 matrix multiplication
: In Linear Algebra the product
between two matrices A and B are defined if A is n by m
and B is m by p. Notationally it is given by
(AB)_{i,j} = 

A_{i,k} B_{k,j}.

MATLAB uses the usual multiplication symbol *
for matrix
multiplication when the two quantities are matrices.
>> A = [1,2;3,4] % A is 2 by 2
>> B = [5,6,7;8,9,10] % B is 2 by 3
>> A*B % answer is 2 by 3
ans=
21 24 27
47 54 61
>> B*A
Warning, Warning Will Rogers % Who said you could do this! Wrong sizes
 transpose
: in Linear Algebra the transpose operator
changes a n by m matrix into an m by n matrix by switching
the indices. In MATLAB it is indicated with the ' sign. A
typical example is to transform a row
vector
into a column
vector.
>> v = [1,2,3] % a row vector
>> v' % a column vector
 vector
or list
: In Linear Algebra a vector is a list of
numbers of a certain size. It can be a row vector such as
>> [1, 2, 3] % the vector (1,2,3)
or a column vector, which in MATLAB is entered in with
>> [1;2;3] % the vector (1)
% (2)
% (3)
In Physics, a vector is a mathematical quantity that represents a
magnitude and a direction. A vector becomes a list of numbers once we
chose a coordinate system, and identify a vector with the directed
line segment from the origin to a point. Often the distinction between
a column vector and a row vector is not made, but it is
important to MATLAB.
Here are some definitions of some terms found in this tutorial and on
the internet: