Basic Math for 16-720
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Basic Math for 16-720. August 23, 2002. 1 Linear Algebra. 1.1 Vectors and Matrices. First, a reminder of a few basic notations, definitions, and terminology …
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Basic Math for 16-720
August 23, 2002
1 Linear Algebra
1.1 Vectors and Matrices
First, a reminder of a few basic notations, de nitions, and terminology:
Unless indicated otherwise, vectors are always column vectors (n1 matrices). The identity matrix
is denoted by I.
The dot product of two column vectors is de ned as u v = uT v
The norm of of a vector is de ned as juj2 = uTu
If is the angle between u and v, then cos = uTv
jujjvj
A matrix A is symmetric if A = AT
The null space of a matrix A is the set of vectors x such that Ax = 0
The rank of A is the dimension of its column(row) space
A n n matrix A is non-singular (A..1 exists) if its rank is n, i.e., det(A) 6= 0
A p p minor of A is an p p sub-matrix extracted from the rows and columns of A. If A is of
rank r < n...
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