Inverse issue?

[ifomenko]

I met something strange

[-MFra-]

Hi

It is wrong to define the matrix operator with square brackets. not [A] but simply A - although it is possible - and many ancient texts define it with square brackets. The inverse of a vector makes no sense.

[LucMeekes]

There's nothing wrong about that. It's the OP's method of marking matrices and vectors.

[LucMeekes · Accepted solution]

It is simply the 'inverse' of each element of your vector (so vectorization is implicit here). That's the only way way Mathcad can produce an answer that is not an error message.

The help on Matrix inverse is:

Matrix Inverse Operator

Keystroke: ^-1

This returns the inverse of a matrix. If M does not have an inverse, you'll see an appropriate error message.

Operands:

• M is a square matrix having an inverse.

Your multiplication A * A^-1 results in 3, because A has three elements.

The symbolic (Maple) processor complains that the matrix should be square...

Success!

Luc

[LucMeekes]

[ifomenko]

Thanks, but it's wrong behavior

[Werner_E]

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@ifomenko wrote:
Thanks, but it's wrong behavior

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Yes, from a math point of view we would expect an error message instead of a result.

To be able to interpret the result we have to know, that Mathcad will switch into automatic (implicit) vectorization whenever the operation will make no mathematical sense when applied to vector or matrices.
Many people find Mathcads implicit vectorization quite convenient but personally I'd prefer to explicitly use vectorization even though Mathcad would apply it implicitly on its own.

As you can see in the screenshot, the symbolic processor is more strict and requires explicit vectorization: