Orthogonal and Orthonormal vectors and its connection with Linearly independent vectors!!

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Why do we need Inner Product? Motivation to study this topic!

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Infinite examples on Inner Product on Polynomial Vector Space.

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Example of an inner product on Matrices which helps us to find angle and length.

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Orthogonal Vectors are Linearly Independent vectors but not conversely. Counterexample as well.

[tusharkantimondal]

Sir in the example 3, I think the matrix 2×3 matrix can't transpose because that is not a square matix, if it is a 2×2 or 3×3 matrix than it can form transpose of that matrix