Sure. There are other applications of arithmetic, but algebra without arithmetic is impossible. A broad knowledge of arithmetic is essential for mastery of algebra.
Linear Algebra
Use equation.
Zero is a number (a scalar quantity without unit) while zero vector (or null vector) is a vector quantity having zero magnitude and arbitrary direction.
When focusing upon abstract algebra, there are many different areas included within this topic such as groups, rings, modules and vector space. These all are part of the sequence to constructing abstract algebra.
Sure. There are other applications of arithmetic, but algebra without arithmetic is impossible. A broad knowledge of arithmetic is essential for mastery of algebra.
in which field vector calculus is applied deeply
"Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another." (from Wikipedia)
It can mean that it is a vector.
Linear Algebra
Use equation.
Zero is a number (a scalar quantity without unit) while zero vector (or null vector) is a vector quantity having zero magnitude and arbitrary direction.
calculus and vector algebra
Because Algebra said so
A. E. Hirst has written: 'Vectors in 2 or 3 dimensions' -- subject(s): Vector algebra, Vector analysis
C. E. Goodson has written: 'Technical algebra with applications' -- subject(s): Algebra 'Technical trigonometry with applications' -- subject(s): Trigonometry
George Mackiw has written: 'Applications of abstract algebra' -- subject(s): Abstract Algebra