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MAAn easy way to calculate the inverse of 3โ๏ธ3 matrix.
@mathxmatrix
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THMatrix multiplication is a fundamental concept in mathematics with real-world applications in physics, engineering, and machine learning. It works by combining two matrices in a structured way: the number of columns in the first matrix must match the number of rows in the second. The result is a new matrix where each element is found by taking the dot product of a row from the first matrix and a column from the second. Unlike simple arithmetic, matrix multiplication isnโt always reversible, order matters, meaning AxB is usually different from BxA . Despite this, it follows predictable rules, such as associativity and distributivity.
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@themathcentral
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MAMental maths #math #study #hack #learn #solve
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PEThe best data scientists I know understand the maths behind the ML algo.
Comment โdataโ ansi will see you the links to the 4 maths resources.
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RAMATRIX cheatsheet mind map
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THInverse of 3ร3 Matrix
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What is the cofactor C_{12} for a 3ร3 matrix?
@thevisualmaths
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TIWhat exactly is matrix multiplication?!
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UNMatrix is a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.
To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. To find each element in the resulting matrix, multiply corresponding elements of a row from the first matrix and a column from the second matrix, then sum the products. This process is repeated for each row of the first matrix and each column of the second matrix to fill the entire product matrix.
This video demonstrates how to multiply two matrices step-by-step:๐
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ME๐ฅ Matrix in 3D โ When the Determinant is Zero
What happens when you apply a 3ร3 matrix to space?
In this animation:
We start with the standard cube formed by the unit vectors iฬ, jฬ, kฬ โ each shown as yellow arrows.
These vectors form the edges of a perfect cube. The determinant of the identity matrix is 1 โ the cube has volume.
Then, we apply a matrix whose determinant is zero.
Watch as the cube collapses! The transformed vectors still span a region, but it loses depth โ it flattens onto a plane.
This means the matrix has squashed 3D space into 2D. Thatโs why its determinant is 0: no volume remains.
Finally, we highlight how each transformed vector corresponds to a column in the matrix โ each vector is just a column, turned into motion.
๐ A zero determinant means no inverse. The transformation is singular โ it crushes space.
๐ Save this if youโre studying linear algebra or want to visualize what matrices do in 3D.
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MRLets hit 100k as soon as possible (excape t the Matrix) Part 1ย |ย Day 1ย
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First Lesson: How Does the Matrix Actually Work?
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How Big Is The Difference?ย
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Follow โฌฉ @mr.freemanx1 if youโre ready to master the real game.
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PEPutting machine learning mathematics prerequisites into context, to better appreciate their significance.
Resources used:
- Deisenroth at al, Mathematics for Machine Learning, 2020
- Goodfellow et al, Deep Learning, 2016
- MathAcademy
@petal.byte
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MAIts Matrix vs Determinant
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