Matrices Vernacular

Single Matrix

The determinant of a square matrix is a number that indicates how that matrix behaves. There are different ways to calculate the determinant depending on the size of the individual matrix. The simplest form concenrs a 2x2 matrix:

The determinant can be negative or zero. A negative determinant means that the volume was mirrored over an odd number of axes. If the determinant is zero, then there is either no unique non-trivial solution, or there are infinitely many.

For a 3x3 matrix, you must multiply the column in a specific sequence. This formula is known as the "Rule of Sarrus":

Alternatively, this same calculation for a 3x3 dimensional matrix can also be mathematically perceived as follows:

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Multiplying Matrices

Next, there are some arithmetical operations which can be performed on multiple matrices. The simplest scenario is when both matrices are symmetrical. Otherwise there are some rules first which must be applied depending on the dimensions of these unsymmetrical matrices:

• The multiplication of matrices is not commutative.
• The overriding rule is that A can only be multiplied by B if the number of columns in A matches the number of rows in B.
• Hence if A which is a mxn dimensional matrix is multiplied by B which is a nxp dimensional matrix, then the resulting product C will be a matrix with mxp dimensions.
• The product of B.A can not be evaluated {or is invalid} if the number of columns in B does not match the number of rows in A.

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Naval Parlor

Largest 🚢 cruise ship in the world 🛳️ is the Icon of the Seas:

• Gross Tonnage = 248'663 GT
• Weight = x tons
• Capacity = 7'600 passengers
• Length = x meters
• Width = x meters
• Max speed = 22 knots or 41 km/h (NB: 🪢 1 knot = 1.86 km/h)

Nasal Anatomy

Your two nasal passages, one on each side of your nose, are interconnected. They are separated by a thin wall called the nasal septum. The nasal septum divides the nasal cavity into two halves, creating a left and right nasal passage.

These passages are connected at the back of the nasal cavity, where they open into the nasopharynx, the upper part of the throat. This interconnected structure allows air to flow through both nasal passages, facilitating breathing and the sense of smell.

Why do watches turn clockwise?

Time keeping devices usually rotate clockwise because they traditionally emulate the direction the shadow of a gnomon revolves on the brass plate of a sundial in the northern hemisphere.🧭

To calibrate the dial depends on your geographical latitude of your location. You need different sundials, depending on where you are on Earth. 🌎

Also you must always ensure that your device {the 12:00 🕛 position} is pointing due North.⬆️The gnomon itself is historically tilted upwards indicating the position of the North star in the sky.⭐️

Note that if you are ever facing the sun 🌞 in the northern hemisphere, it is never North!

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The Planck Mass

Remember that m=E/c²=eV/c² because an electronvolt is also a measure of Energy.

A photon of light has no mass which is why it can travel at the speed of light.

The least massive & illusive particle is a Neutrino denoted by a V which has a mass of 0.8 eV/c² and therefore can only travel at less than the speed of light.

Visible matter is made up of atoms. An electron denoted by e^- has a negative charge of -1 and a mass of 511'000 eV/c² = 0.511 MeV/c² (half a million times heavier than V).

The Up Quark u is a fundamental particle with a mass of 1.9 MeV/c² and a charge of +²/₃.

The Down Quark d is also a fundamental particle with a mass of 4.4 MeV/c² and a charge of -¹/₃.

A Proton p⁺ with a positive charge of +1 consists of 2u+1d (held together by an unknown number of massless gluon particles) and has a mass of 938.27 MeV/c².

A Neutron particle n⁰ with a neutral charge of 0 consists of 1u+2d (held together by an unknown number of massless gluon particles) and has a mass of 939.57 MeV/c².

By arithmetically adding up the masses of u & d, you will obtain only 1% of the actual masses of p⁺ & n⁰.

The 99% missing mass of these elementary particles is a result of the Quantum Chromodynamics Binding Energy from the gluons. Although they have no mass, gluons possess energy which is the strong force holding the 3 quarks together.

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The Planck mass = 1.22x10¹⁹ GeV/c².

The Planck mass is the mass of a hypothetical particle called the Planck particle which is a tiny black hole with a radius of 1 Planck length.

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