John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Discrete Math

Irrational Numbers: Importance And Examples In Mathematics, Geometry, Calculus & Beyond.

Irrational Number a number that can NOT be expressed as a ratio of two integers or as a repeating or terminating decimal – Pi or any square...

John Rhodes
June 21, 2023
Discrete Math

Logical Equivalence In Mathematics: Propositional And Truth-Functional Equivalence Explained

Logical Equivalence Two statements are logically equivalent if they imply one another; contrapositive of S = S; inverse of S = converse of S In logic, logical...

John Rhodes
June 21, 2023
Discrete Math

Master The Art Of Divisibility: Learn Effective Rules To Easily Determine Number Divisibility

Divisibility The ability for one number to be divided by another number without a remainder Divisibility is the property of a number that allows it to be...

John Rhodes
June 21, 2023
Linear Algebra

Infinite Inner Products On R^N: Debunking The Common Misconception – A Comprehensive Guide On Varying Definitions Of Inner Products In Vector Spaces

there is exactly one inner product on the vector space R^n 0 This statement is not true. In fact, there are infinitely many inner products on the...

John Rhodes
June 21, 2023
Linear Algebra

Inner Products: Linearity, Conjugate Symmetry, And Positive Definiteness In Vector Spaces

an inner product is a scalar valued function on the set of ordered pairs 1 of vectors in a vector space that satisfies three key properties: linearity...

John Rhodes
June 21, 2023
Linear Algebra

The Limitations Of The Dot Product: When = Then Y=Z Is Not True

if = then y=z in general 0 The statement = then y=z is not true in general. In general, = x1y1 + x2y2 + … + xnyn,...

John Rhodes
June 21, 2023
Linear Algebra

Addition Of Elementary Matrices: Properties And Examples In Linear Algebra

the sum of two n x n elementary matrices is still an elementary matrix 0 Let’s first define what an elementary matrix is. An n x n...

John Rhodes
June 21, 2023
Linear Algebra

Exploring Non-Elementary Matrices: Why The Product Of Two Elementary Matrices Is Not Always Elementary

the product of two n x n elementary matrices in general is not necessarily an elementary matrix 1 An elementary matrix is a matrix obtained from an...