WHEN most of us hear the word "matrix", our minds dart back to the four Matrix movies featuring all-round nice guy Keanu Reeves, released between 1999 and 2021.
But if we shift our focus from the ominous, thankfully fictional premise of Reeves' movies, matrices in the real world are helpful tools for mathematical manipulation.
A matrix is an array of numbers (or symbols or elements) arranged in horizontal rows and vertical columns.
In 1850, the English mathematician James Joseph Sylvester (1814 –1897) coined the term "matrix" for a rectangular array of so-called mathematical determinants. Note: A determinant is a single number calculated from a square matrix.
Eight years after Sylvester came up with the term, his friend and fellow mathematician Arthur Cayley founded the branch of mathematics known as matrix algebra.
In Cayley's 1858 paper entitled A Memoir on the Theory of Matrices, he first treated matrices as mathematical objects in their own right.
His paper explained how to add and multiply matrices and invert a matrix.
Cayley's work inadvertently laid the foundation for something esoteric and immensely practical barrelling down the pipeline in the final month of the 19th century through to the first quarter of the 20th.
Between December 1900 and 1924, quantum physics germinated and blossomed through the work of physicists like Max Planck (for blackbody radiation), Albert Einstein (for quantised light), Niels Bohr (for the structure of the hydrogen atom) and Louis de Broglie (who postulated matter, like light, has wavelike properties).
That fertile quarter century was dominated by what became known as the "old quantum theory", built upon brilliant yet patchwork rules that attempted to understand nascent quantum mechanics within the more mature superstructure of classical mechanics developed by historical giants like Galileo Galilei, Christiaan Huygens and the incomparable Isaac Newton.
The work of Planck, Einstein, Bohr and de Broglie subsequently slotted elegantly into place with a coherent theory in 1925–26 developed by Werner Heisenberg, Max Born and Pascual Jordan, who used matrices to develop matrix mechanics, the first complete and internally consistent formulation of quantum mechanics.
VALUE OF A MATRIX
The rectangular (possibly square) structure of a matrix allows for manipulation of information — any information — across different dimensions.
That's why we are exploring the value of a matrix within this "Money Thoughts" column.
Consider a person's retirement plan.
It is common for my fellow licensed financial planners and me to distil retirement planning to a single ringgit or US dollar quantity, namely the target size of our nest egg. But a single number is just a dot on a numerical plane.
If we were to start with one such number, say our net worth today, and then consider the targeted size of a future nest egg, we would then have — thanks to Euclid — a single line connecting those two dots.
Intuitively, we know that such a line, which is one dimensional, cannot hold all the information needed for a holistic financial plan of a multidimensional person. What might we then do?
Take a page out of matrix algebra and at least qualitatively consider the other relevant dimensions of living well in general and, therefore, specifically living well in retirement.
How might that look?
Matrix mechanics helps us handle simultaneous changes across different dimensions. But, frankly, doing so quantitatively is beyond most of us.
Yet grasping the different dimensions of our lives can be done qualitatively. So, let me leave you with some pointers:
1. If we take too little investment risk, we will most likely experience purchasing power erosion;
2. In full-blown retirement, our active income falls to zero. So, ideally, we should have acted years before to grow our passive income;
3. But leaping back in time is not possible (At least for now). So, for those who are inadequately prepared for retirement, working later than the official retirement age is another — more practical way — of extending our working years and shortening the post-retirement period;
4. Sadly, when retirement arrives, health tends to slip, too, because of advancing years. So, money should be spent on regular medical checkups, medication, gym memberships and sports equipment;
5. The "Law of the Excluded Alternative" dictates that as we spend capital or passive income on maintaining our health or decelerating our decline, we will have less cash for other facets of life; and
6. A complete financial plan encompasses Wealth Protection, Wealth Accumulation and Wealth Distribution (use the mnemonic P-A-D).
All three dimensions could be represented by a matrix that helps us realise if too little is spent on insurance, risk exposure grows too high, and if too much is spent on insurance, too little will be left to build a large nest egg.
If excessive parsimony is exercised, our retirement years will be miserable and way too much money might be left to beneficiaries.
Bottomline: We are complex, multidimensional beings and should not merely live on a dimensionless financial dot or just traverse a mono-dimensional filament.
Decide if a personally crafted matrix covering all vital dimensions of your life might be a useful mental model for you and your satellite system of experts to track, analyse, tweak, cherish and celebrate.
© 2026 Rajen Devadason
Rajen Devadason, CFP, is a Securities Commission-licensed Financial Planner, professional speaker and author. Read his free articles at www.FreeCoolArticles.com; connect with him on LinkedIn at www.linkedin.com/in/rajendevadason, or via rajen@RajenDevadason.com. You may also follow him on X @Rajen Devadason and on YouTube (Rajen Devadason).
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