Linear algebra, vector spaces, eigenvalues and eigenvectors, and linear applications.

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From 22 £ /h

List of lessons

1. Vector Spaces & Subspaces
Key concepts: Understanding the definition of vector space and the ten conditions (Vector Space Axioms) to prove that a set with addition and multiplication operations in its standard form a vector space.
Linear Independence & Dependence: Testing whether vectors are linearly independent or dependent on each other.
Span, Basis & Dimension:
Determine the generative span of the space.
Finding the basis and dimension of different spaces (such as vector spaces \mathbb{R}^n, matrices M_{m \times n}, and polynomials P_n).
Subspaces: Subspace conditions, finding the null space, column space, and row space of matrices.
2. Linear Transformations and Applications
Definition and properties: Proving the linearity of applications and determining the Standard Matrix Representation.
Kernel and Range:
Calculate the kernel (Kernel/Null Space) and image (Image/Range) for conversion.
Applying the Rank-Nullity Theorem and calculating rank and nihilism.
Change of Basis: Transition Matrices and how to represent the same linear transformation under different bases and families.
3. Eigenvalues & Eigenvectors
Characteristic Equation: Finding the eigenvalues of \lambda by solving the equation \det(A - \lambda I) = 0.
Eigenvectors and Eigenspaces: Finding the eigenspace associated with each eigenvalue by solving the homogeneous system (A - \lambda I)\vec{v} = \mathbf{0}.
Diagonalization:
Diagonalizability Condition Test.
Formulating the decomposition of diagonal A = PDP^{-1} to facilitate the calculation of matrix powers A^k and the solving of systems of differential equations.
Orthogonal Diagonalization: For symmetric matrices and the application of Spectral Theorem.

Location

Online from Egypt

About Me

I am a university teaching assistant and economic researcher specializing in government research centers. I provide simplified explanations of econometrics, statistics, finance, and economics, emphasizing in-depth understanding and practical application. I help students grasp concepts, complete assignments, and prepare for exams. I also offer training in using EViews, Stata, SPSS, and Excel, as well as data analysis, interpreting statistical results, and writing academic papers. I ensure that sessions are interactive and tailored to each student's needs, with ongoing support until optimal results are achieved.

Education

I am a university lecturer specializing in econometrics, statistics, economics, finance, and business administration. I provide professional educational sessions for students of public universities, private universities, and foreign universities, as well as graduate students and researchers.

Experience / Qualifications

Bachelor of Statistics from the Faculty of Economics and Political Science, Cairo University
Experience in teaching at more than one private Egyptian university, as well as in the research field at governmental and private research centers.

Age

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Beginner

Intermediate

Advanced

Duration

60 minutes

The class is taught in

English

Arabic

Skills

Math

Numerical analysis

Algebra

Availability of a typical week

(GMT -04:00)

New York

Online via webcam

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

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► EXPERT STATISTICS, DATA ANALYTICS, MACHINE LEARNING & AI TUTOR FROM SWITZERLAND
► UNIVERSITY, FOUNDATION, IB, A-LEVEL & INTERNATIONAL SCHOOL SUPPORT

I completed my Master’s degree in Business Information Systems at a Swiss University of Applied Sciences, where my academic background strongly combined mathematics, statistics, data analysis, analytical thinking and problem-solving. This technical and data-oriented foundation shaped the way I teach today: clearly, logically and with a strong focus on real understanding.

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I mainly use R for statistical analysis, data handling, visualisation and practical exercises. My goal is not only to help students calculate results, but to make sure they understand what the results mean and how to explain them correctly.

► STATISTICS, DATA ANALYTICS & AI SUPPORT

► STATISTICS & PROBABILITY
I help students understand descriptive statistics, probability, random variables, distributions, sampling, confidence intervals, hypothesis testing, p-values, correlation, regression and statistical interpretation. My lessons focus on explaining the logic behind each method, not just applying formulas.

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► I FOCUS ON REAL STATISTICAL UNDERSTANDING.
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Difficult formulas, tests and models are broken down into simple, logical parts so students can follow the reasoning clearly.

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► Interactive whiteboard
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► MAIN TOOL: R
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► FORMAT: Online tutoring from Switzerland
► FOCUS: Statistical understanding, R practice, interpretation, exam preparation, assignments, projects and long-term analytical confidence.

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What I cover:

GCSE Maths (all exam boards — AQA, Edexcel, OCR)
A-Level Maths and Further Maths
University-level Maths for engineering and science students
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I can assist you with:
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In this course you will Learn Math from Scratch Addition, Subtraction,Multiplication,Division,Fractions,Decimals,Statatics,Probability,Word Problems,Trignometry,Surface Areas,Shapes,2D and 3D

This Course last for 6 months

If you complete this course you will become perfect in Foundation of Mathematics...which will help you in future Classes