Determinants and matrices, they look alike. Their similarities caught many unaware and results in "excitements" and much interests.
Both contain numbers within. But ......
- determinants are bounded by two straights lines whereas matrices are by square braces
- determinant resulted in a single numerical value, whereas matrices are sets of numbers grouped within the braces
- determinant can be extracted from matrix, but not the other way round
- there are inverse matrix but not inverse determinant
- a scalar multiplier affects only a single row or single column of a determinant, but affects all the numbers within a matrix
The differences are aplenty. But those listed above are the least any maths students or person should know.
Why create such topics to excite maths learners?
Answer: So that maths will be made interesting and challenging (... the informal reply)
With open mindedness, maths is a very fantastic subject to learn and train for. It carries many hard works and beautiful thinking. Thoughts that are simple yet abstract at times.
Any more fun? ..... You are the answer!
.
There cannot be a meaningful comparison between matrices and determinant.
ReplyDeleteA matrix is an independent quantity whereas a determinant can only be defined for a given matrix.
One can talk of differences like determinant is a scalar, matrix is a vector. Determinant is a single quantity, matrix contains many elements but these are not meaningful as one cannot compare different types of quantities.
You can compare two brands of fan but u can't compare fan and air. Though there are differences like fan is solid, air is a gas, these are not meaningful as the quantities are of different type.
- Thiyagaraj, Chennnai