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How Does a Straight Line Determine Dimension? | #SoME3 Animation vs. Math |Animated Visuals to describe algebraic fundamentals like Linearity, Linearly Dependent & Independentness, Basis and Dimension. ...

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How Cartesian Product Introduces Dimension *Cartesian Coordinates, Cartesian Product & Introduction to Dimension*This is the third lecture of our Lecture Series *"EUCLIDEAN SPACES: a geometric journ...

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What is Distance? It’s not the difference between two points #SoME3 🆕 *Complete Lecture Series, Assignments, and necessary Study Materials*: https://reanlea.com/courses/euclidean-spaces/✍️ Submit a *Feedback Form* : http...

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Prove 🎯🎯🎯 it ...

Prove that - the space of continuous functions C[-1,1] with 1-norm is Cauchy but not Complete.

Guess the nature of transformation🎯🎯🎯...

What is the Geometry of Euclidean Space? Mathematics & Physics scholars must know.
It is on YouTube right now.

Euclidean Space: a journey from dot to distance & metric; vector, inner product & Spaces

Course Outline::

Vector, Distance & Metric

Overview on the difference between static point and vector
Fundamental properties of distance and their geometric interpretation
Defining the metric by generalizing distance between two vectors

1+1 and Vector Spaces

Defining 1+1 in a collection of vectors and how -(-1) becomes 1
Roles of these two identities on vector addition and scalar multiplication
Vector space and their properties

Cartesian Product, Vector Addition & Coordinate System

Defining Cartesian Product
Construction of a new space using Cartesian Product
Overview on how vector addition is associated with the cartesian product in coordinate representation of any vector in that space

Dimensions & Linearity

Defining a function and geometric overview of its linear properties
Geometric representation of linearly dependent and independent vectors
Defining bases and dimensions

Pythagoras Theorem & Component of Vectors

Geometric proof of Pythagoras Theorem
Determining norm or length of a vector
Notion of vector addition and components

Projection, Inner Product & Euclidean Spaces

Representation of projection and generalization
Defining inner products and geometric representation of all its properties
Defining Euclidean Spaces

Norms & Law of Cosines

Defining norms w.r.t inner product
Finding out relation among norm, inner product, Pythagoras theorem and law of cosines
Representation of inner product w.r.t coordinates

Cauchy-Schwarz Inequality & Metric Spaces

Geometric proof of Cauchy-Schwarz inequality
Proof of Triangle inequality for vectors and distances in n-dimensional spaces
Notion of d–infinite metric

link : https://reanlea.com/courses/euclidean-spaces/

"Euclidean Space: a journey from dot to distance & metric; vector. inner product & spaces"
a fully animated course (inspired by 3blue1brown ) is now ready for pre-access at reanlea.com . So, if you're willing to watch it, please let me know. It'll be free for the first 20 enthusiasts...

And please share it to help others ... and let's make the team for new ideas to express in Mathematics ...

On the way of proving "Cauchy Schwarz Inequality" geometrically. Can you prove it using all the information provided ?

Geometric representation of "Inner Product is Symmetric".

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How Cosine plays a role in the symmetricity of Inner Product ( copy of that clip)

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