diff --git a/README.md b/README.md
index 36a2777..27aebb1 100644
--- a/README.md
+++ b/README.md
@@ -4,3 +4,20 @@
 [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://HolyLab.github.io/ScaleInvariantAnalysis.jl/dev/)
 [![Build Status](https://github.com/HolyLab/ScaleInvariantAnalysis.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/HolyLab/ScaleInvariantAnalysis.jl/actions/workflows/CI.yml?query=branch%3Amain)
 [![Coverage](https://codecov.io/gh/HolyLab/ScaleInvariantAnalysis.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/HolyLab/ScaleInvariantAnalysis.jl)
+
+This package provides tools for numerical analysis under conditions where the
+underlying mathematics is scale-invariant. We work on computers with finite
+precision, so operations like matrix-multiplication and matrix-division are
+expected to have some error. However, naive estimates of the error, based on
+quantities like `norm(x)`, may not be scale-invariant.
+
+For example, if `H` is a diagonal nonnegative (Hessian) matrix (i.e., a rank-2
+covariant tensor), with a change-of-scale in the variables all such `H` are
+equivalent to the identity matrix. Therefore we might think that its [condition
+number](https://en.wikipedia.org/wiki/Condition_number) should in fact be 1.
+This package provides tool to calculate condition number, as well as several
+other quantities, under conditions of scale-invariance.
+
+See the
+[documentation](https://HolyLab.github.io/ScaleInvariantAnalysis.jl/dev/) for
+more information.
diff --git a/docs/src/index.md b/docs/src/index.md
index c912ce0..9aebb9e 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -36,9 +36,9 @@ machine precision. This does not seem entirely consistent with common
 expectations of working with matrices with large condition numbers.
 
 Under a coordinate transformation `x → [x[1], x[2]/10^4]`, `H` becomes the
-identity matrix which has a condition number of 1, and this reflects our actual
-experience with operations involving `H` better than the standard condition
-number. This package provides a scale-invariant analog of the condition number:
+identity matrix which has a condition number of 1, and this better reflects our
+actual experience with operations involving `H`. This package provides a
+scale-invariant analog of the condition number:
 
 ```jldoctest example; filter = r"1\.0\d*" => "1.0"
 julia> using ScaleInvariantAnalysis