Transposition

Transposition.mp3
Transposition.mp4
Transposition-Pt-2.mp3
Transposition-Pt-2.mp4
Transposition-intro.mp3

[Intro]
Transposition
(Changed condition)

[Verse 1]
Do you believe
(Black is white)
Can you conceive
(That’s not right)

[Chorus]
Exclamation (Point!)
Formation (Adjoint)
Supposition
(Transposition)

[Bridge]
(Changing your sign)
In a changing time

[Verse 2]
Do you think you know
(White is black)
Well, there ya go
(… wisdom lack)

[Chorus]
Exclamation (Point!)
Formation (Adjoint)
Supposition
(Transposition)

[Bridge]
Overrule intuition
(Mathematician)
(Changing your sign)
In a changing time

[Outro]
Exclamation (Point!)
Formation (Adjoint)
Algebraic transposition
(Do you suppose)
Matrix transpose
(Flipping our lid)
Yes… yes, we did

ABOUT THE SONG

In math, to “transpose” means to switch the rows and columns of a matrix or, in algebra, to move a term from one side of an equation to the other by changing its sign. Transposing a matrix is often shown with a superscript ‘T’ (ATcap A to the cap T-th power 𝐴𝑇) and involves flipping the matrix over its main diagonal. In an equation, moving a term across the equals sign is a form of transposition that helps in solving for a variable.

Matrix transpose

What it is: Switching the rows and columns of a matrix.
How it works: The element in the first row and first column of the original matrix becomes the element in the first row and first column of the new matrix. The element in the first row and second column of the original becomes the element in the second row and first column of the new matrix, and so on.
Result: A

2×32 cross 3

2×3

matrix will become a

3×23 cross 2

3×2

matrix after transposing.

Algebraic transposition

- What it is:
  
  Moving a term from one side of an equation to the other by performing the inverse operation on both sides.

How it works:

When you move a term, you change its sign. For example, if you have

7x=4x−127 x equals 4 x minus 12

7𝑥=4𝑥−12

, you can transpose the

4×4 x

4𝑥

by subtracting it from both sides:

7x−4x=-127 x minus 4 x equals negative 12

7𝑥−4𝑥=−12

Result:

This helps isolate variables to solve the equation. In the example, this becomes

3x=-123 x equals negative 12

3𝑥=−12

From the album “Lulu“