Matrix Notation
Here, we describe how symbols are used on the Stat Trek web site to represent vectors, matrices, and other matrix algebra entities.
Vectors
Bold-face, lower-case letters refer to vectors; and italic lower-case letters refer to vector elements. For example,
a and x refer to vectors a and x, respectively.
ai refers to the ith element in vector a.
General Matrices
Bold-face, capital letters refer to matrices, italic capital letters refer to matrix elements, and subscripts reveal matrix dimension. For
example,
A and X refer to matrices A and X, respectively.
Aij refers to the element in row i and column j of matrix A.
Aij refers to an i by j matrix A.
Special Matrices and Matrix Properties
Special matrices are represented by special notation. For example,
A' refers to the transpose of matrix A.
I refers to an identity matrix.
In refers to an n x n identity matrix.
1 refers to the sum vector, a column vector having all of its elements equal to one.
1n is a 1 x n sum vector.
|A| refers to the determinant of matrix A.
x refers to a matrix of deviation scores derived from the raw scores of matrix X.
Note: Like vectors, deviation score matrices are often denoted by a lower-case, boldface letter, such as x. This can cause confusion, bu
usually the meaning is clear from the context.
Elementary Operations
In many references, including this site, you will encounter a compact notation to describe elementary operations. That notation is show
below.
Ri <--> Rj means to interchange rows i and j of a matrix.
Here, we describe how symbols are used on the Stat Trek web site to represent vectors, matrices, and other matrix algebra entities.
Vectors
Bold-face, lower-case letters refer to vectors; and italic lower-case letters refer to vector elements. For example,
a and x refer to vectors a and x, respectively.
ai refers to the ith element in vector a.
General Matrices
Bold-face, capital letters refer to matrices, italic capital letters refer to matrix elements, and subscripts reveal matrix dimension. For
example,
A and X refer to matrices A and X, respectively.
Aij refers to the element in row i and column j of matrix A.
Aij refers to an i by j matrix A.
Special Matrices and Matrix Properties
Special matrices are represented by special notation. For example,
A' refers to the transpose of matrix A.
I refers to an identity matrix.
In refers to an n x n identity matrix.
1 refers to the sum vector, a column vector having all of its elements equal to one.
1n is a 1 x n sum vector.
|A| refers to the determinant of matrix A.
x refers to a matrix of deviation scores derived from the raw scores of matrix X.
Note: Like vectors, deviation score matrices are often denoted by a lower-case, boldface letter, such as x. This can cause confusion, bu
usually the meaning is clear from the context.
Elementary Operations
In many references, including this site, you will encounter a compact notation to describe elementary operations. That notation is show
below.
Ri <--> Rj means to interchange rows i and j of a matrix.
