Mahesh Anigol’s Reviews > Introduction to Linear Algebra > Status Update

1. Matrix multiplication, explaining how it generalizes the dot product and is used to represent linear equations (AX=B),
2. The matrix multiplication is not necessarily commutative (AB ≠ BA),
3. The distributive and associative laws for matrix products,
4. The relationship between products and transposes is given by ᵗ(AB) = ᵗB ᵗA,
5. The inverse of a square matrix (A⁻¹) is a matrix where AA⁻¹ = A⁻¹A = I.

1. Definition of a Matrix,
2. Examples and Interpretation,
3. Types of Matrices,
4. Matrix operations,
5. Transpose of a Matrix

1. Definition of a Plane.
2. Normal Vector,
3. Equation of a Plane,
4. Relationships between Planes,
5. Intersection of a line and a plane,
6. Equation of a Plane through 3 points,
7. Distance between a point and a plane,
8. Exercises.

1. Definition of Parametric Equation,
2. Physical Interpretation (Motion).
3. Line Segment Between Two Points
4. Relation to Ordinary Equation (2-Space)
5. Higher Dimensions and Non-Uniqueness of Representation.

1. Definition of Norm (or Magnitude)
2. Geometric Region
a. Open disc, Closed Disc, Circle
b. Open ball, Closed ball, Sphere
3. Properties of the Norm
4. Perpendicularity and Norms.
5. Projections
6. Geometric Interpretation of Scalar Product
7, Key Inequalities
a. Schwarz's Inequalities
b. Triangle Inequalities.

1. Scalar Product, Dot Product,
2. Properties of Scalar Product,
2. Conditions for Orthogonality Between Vectors