C++ GDI: I am seeking explanation for color matrix such that I can create any color manipulation mask

I am trying to implement an application that can manipulate the background screen color attributes through a transparent window. Basically trying to recreate Color Oracle. I am progressing here through C++:GDI+ resources. This GDI has a Color Matrix concept. I am able to create filters for greyscale(as shown in the example in the last hyperlink), brightness tweaking, saturation tweaking; However, as advanced use cases such as color blindness filter, blue light filter, contrast tweaks - I am using the hit-n-trial approach, It will be much efficient if anyone can take me in the right direction to learn fundamentals of this color matrix.

Example Matrix is shown below which boosts saturation by a small factor while restricting brightness component.

MAGCOLOREFFECT magEffectSaturationBoost =
    { { // MagEffectBright
        {  1.02f,   0.0f,   0.0f,  0.0f,  1.0f },
        {   0.0f,  1.02f,   0.0f,  0.0f,  1.0f },
        {   0.0f,   0.0f,  1.02f,  0.0f,  1.0f },
        {   0.0f,   0.0f,   0.0f,  1.0f,  0.0f },
        {  -0.1f,  -0.1f,  -0.1f,  0.0f,  0.0f }
      }
    }
    // Using the Matrix
    ret = MagSetColorEffect(hwndMag, &magEffectSaturationBoost);

It will be much efficient if anyone can take me in the right direction to learn fundamentals of this color matrix.

Each color vector is multipled by 5x5 matrix, to make it possible color vector is 5 elements long - the fifth element is a dummy one, this allows to perform additional operations on colors (rotation, scaling, ...).

In your example each color component is multiplied by 1.02f making color brighter, after multiplication - from each color component 0.1 value is subtracted.

You can find full explanation here:

https://learn.microsoft.com/en-us/windows/win32/gdiplus/-gdiplus-using-a-color-matrix-to-transform-a-single-color-use

and:

https://learn.microsoft.com/en-us/windows/win32/gdiplus/-gdiplus-coordinate-systems-and-transformations-about

Few more links:

https://docs.rainmeter.net/tips/colormatrix-guide/

https://www.integral-domain.org/lwilliams/math150/labs/matrixcolorfilter.php