I would like to add to Narm's answer here and have added the same as a comment under her answer.
Basically the datatype of the value assigned to [(value)] should match the datatype of the [value] attribute used for the mat-options. Especially if some one populates the options using an *ngFor as below
<mat-form-field fxHide.gt-sm='true'>
<mat-select [(value)]="heroes[0].id">
<mat-option *ngFor="let hero of heroes" [value]="hero.id">{{ hero.name }}</mat-option>
</mat-select>
</mat-form-field>
Notice that, if you change the [(value)]="heroes[0].id" to [(value)]="heroes[0].name" it won't work as the data types don't match.
These are my findings, please feel free to correct me if needed.