[Verse 1]
Take some vectors from your space
Mix them up with scalar weights
Every combo that you make
Forms the span that they create
It's the smallest room they need
Every linear recipe
[Chorus]
Span is all combinations flowing
Independence means no throwing
Any vector from the crew
Basis gives you something new
Dimension counts the freedom's measure
Linear algebra's hidden treasure
[Verse 2]
When your vectors stand alone
None can claim another's throne
If one equals all the rest
Then dependence is confessed
But independence means they're clean
No redundant parts between
[Chorus]
Span is all combinations flowing
Independence means no throwing
Any vector from the crew
Basis gives you something new
Dimension counts the freedom's measure
Linear algebra's hidden treasure
[Bridge]
Basis is the perfect team
Independent yet complete
Spans the whole space like a dream
Makes representation neat
Every vector writes one way
In this chosen display
[Verse 3]
Count the basis, find dimension
Degrees of freedom's pure intention
R-three needs exactly three
Polynomials need one more than degree
Matrix spaces multiply
Rows and columns reaching high
[Chorus]
Span is all combinations flowing
Independence means no throwing
Any vector from the crew
Basis gives you something new
Dimension counts the freedom's measure
Linear algebra's hidden treasure
[Outro]
Zero space has dimension nil
Perfect bases always will
Share the same essential count
That's what dimensions all about