docs(docs): update getting started

Author: AnzhiZhang

Diff for: docs/src/manual/getting-started.md

@@ -2,8 +2,88 @@
 
 ## Installation
 
-TypedMatrices.jl is a registered package in the Julia package registry. To install it, you can use the Julia package manager. From the Julia REPL, type `]` to enter the Pkg REPL mode and run:
+TypedMatrices.jl is a registered package in the Julia package registry. Use Julia's package manager to install it:
 
 ```julia-repl
-pkg> add Documenter
+pkg> add TypedMatrices
+```
+
+## Usage
+
+Use the package:
+
+```@repl getting-started
+using TypedMatrices
+```
+
+You can list all matrices available with [`list_matrices`](@ref):
+
+```@repl getting-started
+list_matrices()
+```
+
+## Creating Matrices
+
+Each type of matrix has its own type and constructors. For example, to create a 5x5 [Hilbert](@ref) matrix:
+
+```@repl getting-started
+h = Hilbert(5)
+```
+
+Most matrices can accept a type parameter to specify the element type. For example, to create a 5x5 Hilbert matrix with `Float64` elements:
+
+```@repl getting-started
+Hilbert{Float64}(5)
+```
+
+Please check [Builtin Matrices](@ref) in [Reference](@ref) for all available builtin matrices.
+
+## Properties
+
+Matrix has properties like `symmetric`, `illcond`, and `posdef`. Function [`properties`](@ref) can be used to get the properties of a matrix:
+
+```@repl getting-started
+properties(Hilbert)
+```
+
+You can also check properties of a matrix instance for convinience:
+
+```@repl getting-started
+properties(h)
+```
+
+To view all available properties, use [`list_properties`](@ref):
+
+```@repl getting-started
+list_properties()
+```
+
+## Grouping
+
+This package has a grouping feature to group matrices. All builtin matrices are in the `builtin` group, we also create a `user` group for user-defined matrices. You can list all groups with:
+
+```@repl getting-started
+list_groups()
+```
+
+To add a matrix to groups and enable it to be listed by [`list_matrices`](@ref), use [`add_to_groups`](@ref):
+
+```@repl getting-started
+add_to_groups(Matrix, :user, :test)
+list_matrices(Group(:user))
+```
+
+We can also add builtin matrices to our own groups:
+
+```@repl getting-started
+add_to_groups(Hilbert, :test)
+list_matrices(Group(:test))
+```
+
+To remove a matrix from a group or all groups, use [`remove_from_group`](@ref) or [`remove_from_all_groups`](@ref). The empty group will automatically be removed:
+
+```@repl getting-started
+remove_from_group(Hilbert, :test)
+remove_from_all_groups(Matrix)
+list_groups()
 ```