diff --git a/src/eigsolve.jl b/src/eigsolve.jl
index 015b7b12..5abb132b 100644
--- a/src/eigsolve.jl
+++ b/src/eigsolve.jl
@@ -282,8 +282,8 @@ end
 
 @doc raw"""
     function eigsolve(A::QuantumObject; v0::Union{Nothing,AbstractVector}=nothing, 
-        sigma::Union{Nothing, Real}=nothing, k::Int = min(4, size(A, 1)), 
-        krylovdim::Int = min(10, size(A, 1)), tol::Real = 1e-8, maxiter::Int = 200,
+        sigma::Union{Nothing, Real}=nothing, k::Int = 1, 
+        krylovdim::Int = max(20, 2*k+1), tol::Real = 1e-8, maxiter::Int = 200,
         solver::Union{Nothing, LinearSolve.SciMLLinearSolveAlgorithm} = nothing, kwargs...)
 
 Solve for the eigenvalues and eigenvectors of a matrix `A` using the Arnoldi method.
diff --git a/src/general_functions.jl b/src/general_functions.jl
index c5635ff3..bc680198 100644
--- a/src/general_functions.jl
+++ b/src/general_functions.jl
@@ -332,9 +332,9 @@ end
     tracedist(ρ::QuantumObject, σ::QuantumObject)
 
 Calculates the [trace distance](https://en.wikipedia.org/wiki/Trace_distance) between two [`QuantumObject`](@ref):
-``T(\rho, \sigma) = frac{1}{2} \lVert \rho - \sigma \rVert_1``
+``T(\rho, \sigma) = \frac{1}{2} \lVert \rho - \sigma \rVert_1``
 
-Note that `A` and `B` must be either [`Ket`](@ref) or [`Operator`](@ref).
+Note that `ρ` and `σ` must be either [`Ket`](@ref) or [`Operator`](@ref).
 """
 tracedist(ρ::QuantumObject{<:AbstractArray{T1},ObjType1}, σ::QuantumObject{<:AbstractArray{T2},ObjType2}) where {T1,T2,ObjType1<:Union{KetQuantumObject,OperatorQuantumObject},ObjType2<:Union{KetQuantumObject,OperatorQuantumObject}} = norm(ket2dm(ρ) - ket2dm(σ), 1) / 2
 
diff --git a/src/negativity.jl b/src/negativity.jl
index be687746..f58223b4 100644
--- a/src/negativity.jl
+++ b/src/negativity.jl
@@ -5,7 +5,7 @@ export negativity, partial_transpose
 
 Compute the [negativity](https://en.wikipedia.org/wiki/Negativity_(quantum_mechanics)) ``N(\rho) = \frac{\Vert \rho^{\Gamma}\Vert_1 - 1}{2}``  
 where ``\rho^{\Gamma}`` is the partial transpose of ``\rho`` with respect to the subsystem,  
-and ``\Vert X \Vert_1=\Tr\sqrt{X^\dagger X}`` is the trace norm.
+and ``\Vert X \Vert_1=\textrm{Tr}\sqrt{X^\dagger X}`` is the trace norm.
 
 # Arguments
 - `ρ::QuantumObject`: The density matrix (`ρ.type` must be [`OperatorQuantumObject`](@ref)).