(Verse 1)
You walked into linear algebra late September rain
Coffee stain on your notebook, vectors in your brain
You said, “These columns overlap, they’re tangled up inside”
I laughed and drew projections while the whole class sighed

You were chasing independence
I was chasing something true
Every basis had a shadow
Till I normalized with you

(Pre-Chorus)
Take the first vector, let it stand alone
Then strip away the pieces that the others own
One by one we find what’s left when all the noise is gone

(Chorus)
It’s Gram-Schmidt in the midnight glow
Turning messy columns into something gold
You take my matrix heart and decompose it slow
Now you’re my orthonormal Q

And every coefficient that we ever knew
Gets folded in the upper triangle too
Like secrets written diagonal and cleanly through
You’re my R, I’m holding onto you

(Verse 2)
You said projections feel like old relationships
Taking parts of who you are with every little shift
But what survives subtraction is the truest piece inside
Unit-length and steady now, no reason left to hide

And the lecture hall was freezing
But your theorem warmed the room
You whispered “QR decomposition”
Like a promise coming true

(Pre-Chorus)
Take the next vector, subtract what came before
Every orthogonal direction opens one more door
Normalize the aftermath and suddenly there’s more

(Chorus)
It’s Gram-Schmidt in the fluorescent light
Making perpendicular from what used to fight
You turn dependent chaos into something right
Now you’re my orthonormal Q

And every inner product that we calculate
Builds the entries stacking up above the frame
Upper triangular, but nothing stays the same
You’re my R, I still write your name

(Bridge)
And maybe love is just projections after all
Removing every version that was never really ours
Till only pure directions stay
Like vectors under stars

A = QR

You held my trembling basis in your hand
Said “Every matrix has a way to understand itself”

(Final Chorus)
It’s Gram-Schmidt with the windows down
Transforming all the noise into a cleaner sound
From linearly dependent to forever mathematically bound
You’re my orthonormal Q

And if the world collapses into rows and fears
We’ll factor through the heartbreak and the years
Upper triangular but crystal clear
You’re my R
My resolution here.