Is ( 1.2, -3.9, 0.0 ) equal to ( 1.2, -3.9, 0.0 )^{T}

No. Column matrices and row matrices are different types of objects, and cannot be equal.

Your previous courses may not have distinguished between row matrices and
column matrices.
They may
not have made it clear that
*geometric vectors* are different
from the *column matrices* that represent them.
These differences
may seem picky at the moment,
but keeping them straight will
help you get through the difficult material to come.

Here is what it takes for two row or two column matrices to be equal:

- Both matrices must be column matrices, or both must be row matrices.
- Both must have the same dimension (number of elements).
- Corresponding elements of the matrices must be equal

Only matrices of the same type can be compared. You can compare two three-dimensional column matrices, or two four-dimensional row matrices, and so on. It makes no sense to compare a three-dimensional row matrix to a three-dimensional column matrix. For example:

( 6, 8, 12, -3 )^{T} | = | ( 6, 8, 12, -3 )^{T} |

( 6, 8, 12, -3 ) | = | ( 6, 8, 12, -3 ) |

( 6, 8, 12, -3 ) | =/= | ( -2.3, 8, 12, -3 ) |

( 6, 8, 12, -3 )^{T} | =/= | ( 6, 8, 12, -3 ) |

( 6, 8, 12, -3 )^{T} | =/= | ( 6, 8, 12 )^{T} |

The characters =/= are used for "not equal". Sometimes the rules are relaxed and one gets a little sloppy about the distinction between row column matrices and column matrices. But keeping the distinction clear is like "strong data typing" in programming languages. It often keeps you out of trouble.