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* Added 'About JMatrix' section
* Updated the 'Table of Contents'
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<h4><a name="table-of-contents" />Table of Contents</h4>
</summary>

- [🪐 About JMatrix](#about-jmatrix)
- [🔌 Installation](#installation)
* [🎯 Prerequisites](#prerequisites)
+ [For Normal Use](#normal-use)
+ [For Building the Project](#build-use)
- [Constructor Summary](#constructor-summary)
* [Matrix()](#cr_matrix-1)
* [Matrix(int, int)](#cr_matrix-2)
* [Matrix(int, int, int)](#cr_matrix-3)
* [Matrix(double[][])](#cr_matrix-4)
* [Matrix.identity(int)](#cr_matrix-5)
* [`Matrix()`](#cr_matrix-1)
* [`Matrix(int, int)`](#cr_matrix-2)
* [`Matrix(int, int, int)`](#cr_matrix-3)
* [`Matrix(double[][])`](#cr_matrix-4)
* [`Matrix.identity(int)`](#cr_matrix-5)
- [Matrix Operations](#matrix-ops)
* [Addition](#matrix-add)
* [Subtraction](#matrix-sub)
Expand All @@ -61,6 +62,8 @@

<!-- TABLE OF CONTENTS::END -->

## <a name="about-jmatrix" /> 🪐 About JMatrix

**JMatrix** is an educational [Java][java-wiki] library and designed to facilitate and simplify [matrix operations][matrix-ops].
It offers a range of intuitive methods to perform common matrix operations with ease, making it an ideal learning tool for high school students exploring [linear algebra][linear-algebra-wiki] concepts.

Expand Down Expand Up @@ -101,7 +104,7 @@ In addition to the fundamental matrix operations, **JMatrix** also includes matr

If you are interested in obtaining the latest stable version of the project, please check the [latest version][latest-ver]. You can download the archived package containing compiled classes from there.

For improved stability and better usability, we highly recommend downloading the archived package that also includes the source files (e.g `jmatrix-<VERSION>_with_sources.jar`).
For improved stability and better usability, we highly recommend downloading the archived package that also includes the source files (`jmatrix-<VERSION>_with_sources.jar`).
This package contains all the necessary documentation about classes, methods, and other aspects related to **JMatrix**, making it easier to explore and understand the project.

### <a name="prerequisites" /> 🎯 Prerequisites
Expand All @@ -122,8 +125,8 @@ If you plan to build the **JMatrix** project, please ensure you have the followi
- Latest version of [**Make/MinGW**][mingw] or [**Maven**][maven].
- [**Git Bash**][git-bash] *(highly recommended for Windows users)*.

> **Note** If you choose to build the project using [Maven][maven], you don't need to install [Python][python].
>
> **Important**
> If you choose to build the project using [Maven][maven], you don't need to install [Python][python].
> However, if you are Windows user and prefer using [Make][mingw] for building, we highly recommend using [Git Bash][git-bash] as the shell environment. The `Makefile` utilizes [Bash][bash-wiki], making it more compatible with [Git Bash][git-bash].
For more detailed instructions on building the project, you can refer to the [:bookmark:Getting Started][get-started] page.
Expand All @@ -133,12 +136,12 @@ Once you have the necessary prerequisites, you can start exploring and using **J
---


## <a name="constructor-summary"></a> Constructor Summary
## <a name="constructor-summary" /> Constructor Summary
There are 5 constructors that can be used for constructing the matrix.
> :man::question: Still don't understand about matrix? Check the [:bookmark:Introduction to Matrix][what-is-matrix] page
> to get little knowledge about matrix before dive into matrix constructor.
### <a name="cr_matrix-1"></a> Matrix()
### <a name="cr_matrix-1" /> `Matrix()`
This constructor doesn't need any arguments, but it would constructs the **Matrix**
with `null` entries or can be called **null matrix**. In this case, the matrix itself can't do any operations until
get initialized and have valid elements. For example:
Expand All @@ -148,7 +151,8 @@ get initialized and have valid elements. For example:
Matrix m = new Matrix();
```

> **Note** Don't be confused with **null matrix** and **zero matrix**.
> **Note**
> Don't be confused with **null matrix** and **zero matrix**.
> **Null matrix** is a matrix that has `null` entries, whereas the **zero matrix** is a matrix with all elements are zero.
>
> <details><summary><b>Examples</b></summary>
Expand Down Expand Up @@ -179,7 +183,7 @@ Matrix m = new Matrix();
</details>
### <a name="cr_matrix-2"></a> Matrix(int, int)
### <a name="cr_matrix-2"></a> `Matrix(int, int)`
How to create **zero matrix**? Don't worry, with this constructor you can construct **zero matrix** with ease.
With just two arguments, each for size of [row][matrix-row] and [column][matrix-col].
The matrix can be called **zero matrix** if all elements inside the matrix is zero.
Expand All @@ -190,7 +194,7 @@ For example:
Matrix m = new Matrix(3, 4);
```
The code above would constructs a new **zero matrix** with size $3 \times 4$. The matrix should looks like this:
The code above will construct a new **zero matrix** with size $3 \times 4$. The matrix will looks like this:
```math
\begin{bmatrix}
Expand All @@ -200,7 +204,7 @@ The code above would constructs a new **zero matrix** with size $3 \times 4$. Th
\end{bmatrix}
```
### <a name="cr_matrix-3"></a> Matrix(int, int, int)
### <a name="cr_matrix-3" /> `Matrix(int, int, int)`
This constructor is similar with [`Matrix(int, int)`](#cr_matrix-2) but with an additional
argument which is the value to filled out the entire elements of constructed matrix. For example:
Expand All @@ -209,7 +213,7 @@ argument which is the value to filled out the entire elements of constructed mat
Matrix m = new Matrix(4, 4, 5);
```
The matrix constructed above should output the same like this:
The constructed matrix above will looks like this:
```math
\begin{bmatrix}
Expand All @@ -220,7 +224,7 @@ The matrix constructed above should output the same like this:
\end{bmatrix}
```
### <a name="cr_matrix-4"></a> Matrix(double\[]\[])
### <a name="cr_matrix-4" /> `Matrix(double[][])`
This constructor is very **RECOMMENDED** for constructing a new [matrix][what-is-matrix].
It because you can declare the entries first, and then you can convert it to **Matrix** object whenever you want.
For example:
Expand All @@ -246,11 +250,12 @@ Matrix m = new Matrix(new double[][] {
});
```
### <a name="cr_matrix-5"></a> Matrix.identity\(int)
### <a name="cr_matrix-5" /> `Matrix.identity(int)`
This constructor would creates new **identity matrix** with size $n \times n$ (the $n$ is from input).
**Identity matrix** itself is a square matrix with ones on the main diagonal and zeros elsewhere. And the **identity matrix** is often denoted by $I$.
> **Note** In code you should avoid using neither $I$ or $i$ for the **Matrix**'s variable name, it because $i$ is often used by `for-loop` statement.
> Instead you can use $mI$ or similar with it.
> **Note**
> In code you should avoid using neither $I$ nor $i$ for the **Matrix**'s variable name, it because $i$ is often used by `for-loop` statement.
> Instead you can use $mI$ or similar with that.
For example:
Expand All @@ -272,9 +277,9 @@ The matrix will looks like this:
```


## <a name="matrix-ops"></a> Matrix Operations
## <a name="matrix-ops" /> Matrix Operations

There are some basic matrix operations you can do with **JMatrix**:
There are some basic matrix operations provided by **JMatrix**:

- [Addition](#matrix-add)
- [Subtraction](#matrix-sub)
Expand All @@ -284,11 +289,12 @@ There are some basic matrix operations you can do with **JMatrix**:

Please refer to [:books: JMatrix Wikis][matrix-ops], for more detailed about matrix operations.

### <a name="matrix-add"></a> Addition
### <a name="matrix-add" /> Addition

:book: **Wiki:** [Matrix Addition][matrix-add]

> **Note** Ensure the two matrices are same dimensions before operating **addition**.
> **Note**
> Ensure the two matrices are same dimensions before operating **addition**.
**Example code:**
```java
Expand Down Expand Up @@ -317,11 +323,12 @@ Matrix k = Matrix.sum(m, n);
\end{bmatrix}
```

### <a name="matrix-sub"></a> Subtraction
### <a name="matrix-sub" /> Subtraction

:book: **Wiki:** [Matrix Subtraction][matrix-sub]

> **Note** Ensure the two matrices are same dimensions before operating subtraction.
> **Note**
> Ensure the two matrices are same dimensions before operating subtraction.
**Example code:**
```java
Expand Down Expand Up @@ -353,7 +360,7 @@ Matrix k = Matrix.sub(m, n);
\end{bmatrix}
```

### <a name="scalar-mult"></a> Scalar Multiplication
### <a name="scalar-mult" /> Scalar Multiplication

:book: **Wiki:** [Scalar Multiplication][scalar-mult]

Expand All @@ -379,11 +386,12 @@ Matrix s = Matrix.mult(m, 5);
\end{bmatrix}
```

### <a name="matrix-mult"></a> Matrix Multiplication
### <a name="matrix-mult" /> Matrix Multiplication

:book: **Wiki:** [Matrix Multiplication][matrix-mult]

> **Note** Ensure the number of [columns][matrix-col] in the first matrix and the number of [rows][matrix-row] in the second matrix are equal before operating matrix multiplication.
> **Note**
> Ensure the number of [columns][matrix-col] in the first matrix and the number of [rows][matrix-row] in the second matrix are equal before operating matrix multiplication.
**Example code:**
```java
Expand Down Expand Up @@ -414,7 +422,7 @@ Matrix mn = Matrix.mult(m, n);
\end{bmatrix}
```

### <a name="matrix-transpose"></a> Transposition
### <a name="matrix-transpose" /> Transposition

:book: **Wiki:** [Matrix Transposition][matrix-tranpose]

Expand Down Expand Up @@ -442,14 +450,14 @@ Matrix mT = Matrix.transpose(m);
```


## <a name="author"></a> Author
## <a name="author" /> Author

**JMatrix** is developed and maintained by [Ryuu Mitsuki][mitsuki31].

As the sole developer of the project, [Ryuu Mitsuki][mitsuki31] responsible for the continuous improvement and updates of the library. He is committed to providing a valuable and user-friendly educational resource for high school students and anyone interested in exploring [linear algebra][linear-algebra-wiki] concepts through the **JMatrix** library and by using [Java](https://www.oracle.com/java).


## <a name="license"></a> License
## <a name="license" /> License

**JMatrix** is licensed under the [Apache License 2.0][apache-2.0]. This license permits you to use, modify, distribute, and sublicense the software, subject to certain conditions.

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