the set of integers

the set of positive integers

the set of complex numbers

the set of real numbers

ⁿ

the set of real-valued n-dimensional vectors

^{m n}

the set of real-valued m by n matrices

?

infinity

Re

real part

Im

imaginary part

?

belongs to

=

equal

?

approximately equal

?

end of proof

?

Kronecker product

I _n

the n n identity matrix

[A] _i,j

the (i, j)th entry of the matrix A

A(i, :)

the ith row of the matrix A

A(: , i)

the ith column of the matrix A

A ^T

the transpose of the matrix A

A ^?1

the inverse of the matrix A

A ^1/2

the symmetric positive-definite square root of the matrix A

diag( a ₁, a ₂, , a _n)

an n n diagonal matrix whose (i, i)th entry is a _i

det (A)

the determinant of the matrix A

range (A)

the column space of the matrix A

rank (A)

the rank of the matrix A

trace (A)

the trace of the matrix A

vec (A)

a vector constructed by stacking the columns of the matrix A on top of each other

A ₂

the 2-norm of the matrix A

A _F

the Frobenius norm of the matrix A

[x] _i

the ith entry of the vector x

x ₂

the 2-norm of the...