Linear Algebra New Notes for BS/MSc

**Scalar**: The quantity that have or posses only magnitude, like mass, work, etc.

**Vector: **The quantities that posses both magnitude and direction are called vector quantities. Like displacement, acceleration, velocity, weight etc.

**Parallel Vector:** Two vectors are considered parallel if and only if they can be obtained by multiplying each of them by a positive scalar.

If they are in same direction then they make zero angle. If they are in opposite direction then they make 180 degree angle.

**Orthogonal Vectors:** If the dot product of two vectors is equal to zero then they are orthogonal vectors.

**Null Vector or zero vector:** A null vector is a vector with zero magnitude. The null vector has an arbitrary direction.

**Unit Vector:** A unit vector, also known as a normalized vector, is a vector whose length is always equal to 1.

The other definitions related to Linear Algebra notes are given in pdf attached below. The definitions like Matrix, Null Matrix, Square Matrix, Rectangular Matrix, Identity Matrix or Unit Matrix, Upper Triangular Matrix, Lower Triangular Matrix, Triangular Matrix, Symmetric Matrix, Skew-Symmetric Matrix, Hermitian Matrix, Skew-Hermitian Matrix, Leading Entry, Echelon form, Reduced Echelon form.

Gratitude goes to Muhammad Zeeshan Khan, who serves as a Visiting Lecturer in Mathematics at the University of Mianwali, for generously sharing these notes (Linear Algebra Notes).

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