✪ Element: Each item in the inner array is called an element of the matrix. Eg, a₁₁
✪ Row: Each item in the main array is called a row. Eg, [a₁₁, a₁₂, a₁₃]
✪ Column: A column is list of items at a specific index from each row in order. Eg, [a₁₁, a₂₁, a₃₁]
1️⃣ Dimension of a Matrix
Dimension of a Matrix is specified as the number of rows and number of columns in the matrix.
2️⃣ Square Matrix
A matrix is called as a "Square Matrix" only if its "number of rows" is equal to its "number of columns".
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.
4️⃣ Upper Triangular Matrix
An "Upper Triangular Matrix" is a square matrix which has only Zeroes (0s) as elements "below" the diagonal elements.
5️⃣ Lower Triangular Matrix
An "Lower Triangular Matrix" is a square matrix which has only Zeroes (0s) as elements "above" the diagonal elements.
6️⃣ Identity/Unity Matrix
An "Identity Matrix" is a diagonal matrix with only 1s as its diagonal elements.
7️⃣ Zero Matrix
A "Zero Matrix" has only Zeroes (0s) as all its elements.
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.
9️⃣ Scalar Multiplication
By doing "Scalar Multiplication", each element of the matrix is multiplied by a scalar value.
1️⃣0️⃣ Matrix Addition
By "Matrix Addition", elements at a specific row and column from 2 matrices are added.
1️⃣1️⃣ Matrix Subtraction
By "Matrix Subtraction", elements at a specific row and column from one matrix is subtracted from the another.
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.
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.
OMISSIONS:
✪ Determinant of a Matrix
✪ Inverse of a Matrix
Because of their complex algorithms which won't fit into an infographic, I omitted these two.
Are you interested in JavaScript contents? I am sharing a lot of materials in Infographics.
⬩Know your final goal
⬩Set a target for spending daily 1 hour minimum.
⬩Research about Python ecosystem (libraries, frameworks, code editors).
P.S: This is my personal roadmap. I could spend 1 to 2 hours daily for learning and practicing. And it took me ~1 year to finish. It may differ from person to person.
➊ Start with a bang: Simple Data Types
Schedule: Month-1
Effort: 1 to 2 hours daily + Normal practice
❍ C/C++
❍ Java
❍ Python
❍ JavaScript
Or, any language of your choice
Stay in top 5% of programmers.
➊ Arrays
➀ Creating an Array
➁ Iterate through Array
➂ Get an Element
➃ Search an Element
➄ Insert Element(s)
➅ Delete Element(s)
➆ Filter an Array
➇ Fetch a Sub-Array
➈ Merging Arrays
➉ Reverse Array
➀➀ Rotate Array
➋ Linked Lists
➀ Creating a Linked List
➁ Iterate through Linked List
➂ Get an Element
➃ Find an Element
➤ Insert Element(s)
➄ At Start
➅ At End
➆ At Anywhere
➤ Delete Element(s)
➇ From Start
➈ From End
➉ From Anywhere
➀➀ IsEmpty
➀➁ Merging Linked Lists
➀➂ Reverse Linked List
➀➃ Check for Cycles
Implement these algorithms for linked lists, double linked lists, circular linked lists, etc.