🔥 MATRIX Operations implemented in JavaScript 🚀
Welcoming you to this super exciting 🧵 where we will implement various matrix operations in JavaScript along with their Complexity Analysis (both Time and Space).
Are you excited to know? 👇
We will cover 👇
🔹 Dimension
🔹 Square Matrix
🔹 Diagonal Matrix
🔹 Upper Triangular
🔹 Lower Triangular
🔹 Identity Matrix
🔹 Zero Matrix
🔹 Transpose Matrix
🔹 Scalar Multiplication
🔹 Matrix Addition
🔹 Matrix Subtraction
🔹 Matrix Multiplication
🔹 Orthogonal Matrix
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0️⃣ Introduction
Matrix is a 2-dimensional (array) arrangement of numbers and it has vast use in Linear Algebra.
Example:
[[a₁₁, a₁₂, a₁₃],
[a₂₁, a₂₂, a₂₃],
[a₃₁, a₃₂, a₃₃]]
Each element in the inner array is called an element of the matrix. Eg, a₁₁
++
Each element in the main array is called a row. Eg, [a₁₁, a₁₂, a₁₃]
A column is formed by taking elements at a specific index from each row in order. Eg, [a₁₁, a₂₁, a₃₁]
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1️⃣ Dimension of a Matrix
Dimension of a Matrix is specified as the number of rows and number of columns in the matrix.
Example:
[[a₁₁, a₁₂],
[a₂₁, a₂₂],
[a₃₁, a₃₂]]
Dimension is 3x2
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2️⃣ Square Matrix
A matrix is called as a "Square Matrix" only if its "number of rows" is equal to its "number of columns".
Example:
[[a₁₁, a₁₂, a₁₃],
[a₂₁, a₂₂, a₂₃],
[a₃₁, a₃₂, a₃₃]]
Here, number of rows is 3 and number of columns is also 3.
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3️⃣ Diagonal Matrix
A "Diagonal Matrix" is a square matrix which has only Zeroes (0s) as its non-diagonal elements (row index = column index).
Diagonal elements can be both Non-Zero and Zero.
Example:
[[5, 0, 0],
[0, 2, 0],
[0, 0, -3]]
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4️⃣ Upper Triangular Matrix
An "Upper Triangular Matrix" is a square matrix which has only Zeroes (0s) as elements "below" the diagonal elements.
Example:
[[5, 6, 7],
[0, 2, 3],
[0, 0, -3]]
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5️⃣ Lower Triangular Matrix
An "Lower Triangular Matrix" is a square matrix which has only Zeroes (0s) as elements "above" the diagonal elements.
Example:
[[5, 0, 0],
[1, 2, 0],
[4, 7, -3]]
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6️⃣ Identity/Unity Matrix
An "Identity Matrix" is a diagonal matrix with only 1s as its diagonal elements.
Example:
[[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
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7️⃣ Zero Matrix
A "Zero Matrix" has only Zeroes (0s) as all its elements.
Example:
[[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]
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8️⃣ Transpose Matrix
A "Transpose Matrix" is formed by converting rows of a matrix into columns (and thus columns into rows).
Dimension of a transpose matrix is exactly opposite of the dimension of the original matrix.
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9️⃣ Scalar Multiplication
By doing "Scalar Multiplication", each element of the matrix is multiplied by a scalar value.
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1️⃣0️⃣ Matrix Addition
By "Matrix Addition", elements at a specific row and column from 2 matrices are added.
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1️⃣1️⃣ Matrix Subtraction
By "Matrix Subtraction", elements at a specific row and column from one matrix is subtracted from the another.
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1️⃣2️⃣ Matrix Multiplication
By "Matrix Multiplication", elements of a row from the first matrix is first multiplied with elements of a column from the second matrix and then summation is taken.
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1️⃣3️⃣ Orthogonal Matrix
A matrix is known as "Orthogonal" when multiplied with its transpose results into an Identity Matrix.
In other words, if transpose of a matrix is equivalent to its inverse, the matrix is orthogonal.
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OMISSIONS:
Inverse and, Determinant of a Matrix are omitted because of time constraints.
But, by now you must be familiar with matrix operations. Can you implement these 2 on your own? If you do, share that here in the reply.
We reached to the end of this 🧵. I hope you enjoyed implementing all these matrix operations in JavaScript.
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See you soon,👋
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