Linear Algebra: Important Definitions and Results

These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. These notes contains important definitions with examples and related theorem, which might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.

• If a vector space $V$ has a basis with $n$ elements, then $n$ is called dimension of $V$.
• If $W$ is a subspace of $V$, then dim(W) = dim(V).
• The span of column of a matrix $A$ is called column space of $A$.
• The span of rows of a matrix $A$ is called row space of $A$.
• If $T:V\to W$ is linear transformation, then $K(T)$, kernel of $T$, is subspace of $V$.
• If $T:V\to W$ is linear transformation, then $R(T)$, range of $T$, is subspace of $W$.

Please click on View Online to see inside the PDF.

• Complex Analysis (Quick Review)
• Group Theory: Important Definitions and Results
• Linear Algebra: Important Definitions and Results
• Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas
• PPSC General Information, Syllabus, Paper Pattern
• PPSC Mock Interview Lecturer Mathematics
• PPSC Paper 2011 (Lecturer in Mathematics)
• PPSC Paper 2015 (Lecturer in Mathematics)
• PPSC Paper 2021 (Lecturer in Mathematics)