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

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From 41 C$ /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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The service includes:
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Solving and analyzing mathematical applications, problems, and exam exercises.
Clarifying and simplifying economic curves and data.
The curriculum is explained in either Arabic or English, depending on the university requirements.
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Interactive sessions with students via Zoom.
Summaries and worksheets to review key concepts before tests.
Support, interaction, and a space to answer any questions during the study period.

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Training in statistical analysis using popular software such as SPSS, Excel, or R.
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Solve past exam papers and focus on the most frequently asked questions.
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